Content-Type: multipart/mixed; boundary="-------------0301120609571" This is a multi-part message in MIME format. ---------------0301120609571 Content-Type: text/plain; name="03-12.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="03-12.keywords" Hamiltonian systems, transport, forced systems, global bifurcations ---------------0301120609571 Content-Type: application/postscript; name="sfjan6la.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="sfjan6la.ps" %!PS-Adobe-2.0 %%Creator: dvips(k) 5.86 Copyright 1999 Radical Eye Software %%Title: sfjan6la.dvi %%CreationDate: Tue Jan 07 09:07:35 2003 %%Pages: 20 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%DocumentFonts: CMBX10 CMR8 CMCSC10 CMMI8 CMSY8 CMR6 CMR10 CMTI10 CMTI8 %%+ CMR7 CMMI10 CMSY10 CMSY7 CMEX10 CMR5 CMMI5 CMMI7 CMMI6 MSAM10 CMSY5 %%+ CMSY6 CMTT8 %%DocumentPaperSizes: a4 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips.exe -P pdf -G0 sfjan6la %DVIPSParameters: dpi=8000, compressed %DVIPSSource: TeX output 2003.01.07:0905 %%BeginProcSet: tex.pro %! /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{ statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0] N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin /FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array /BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2 array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get }B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub} B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr 1 add N}if}B/CharBuilder{save 3 1 roll S A/base get 2 index get S /BitMaps get S get/Cd X pop/ctr 0 N Cdx 0 Cx Cy Ch sub Cx Cw add Cy setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx sub Cy .1 sub]{Ci}imagemask restore}B/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put }if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{ bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{ SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{ userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X 1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4 index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N /p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{ /Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT) (LaserWriter 16/600)]{A length product length le{A length product exch 0 exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot} imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M} B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{ p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end %%EndProcSet %%BeginProcSet: alt-rule.pro %! % Patch by TVZ % Makes dvips files draw rules with stroke rather than fill. % Makes narrow rules more predictable at low resolutions % after distilling to PDF. % May have unknown consequences for very thick rules. % Tested only with dvips 5.85(k). 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89b65dd6c7492544f9867e5d67a726c12eae871116f237612f3355ca6b3d9559 26ec52116347d5a5408d215ba61f8bc6b3eec0e6b901e474063c4f3322a5c20e 9232cb3b04f907d69e378b250234c50d5271f3b954e05463a651203c489fb616 dcc2b8777a80990e7960f6a18e2c840eb6f823956b0e097ba8122c609757f7cd 0d6904233f3c082a085291a8f86cfdca31e2c7e36a54c15198a21479e401bd6a f02bdfdf7da0d60bfd7c3d8a4457d596383fc31140037e98243871244ad1f76f 7bf43dc9d236f6b620b18450712804f0ae9b7efe15146ee5ff2b5dcf4de539b8 c1b887df902e11924c4438f040dfff1ff3e68e7710bcd87a010ef75478a9f5c7 9dfdd617919b2db53175256d33df3d146a3e8f06000a283a585c4b12f9f29515 b19f46baf649c822e11f94fc7ed4a307fde9828669851f6d8c5ddba526f9880c 38a2ca032c3b81b949bc28603ff671d06ae780d31e2e78b49461842a531df6d2 b91331d8b7869b92a67849d98ca61ff6ba01ddea65d44f23f224f7d2fd0e0cb7 15bd5086c005aff9bddc69cb23b875b8ad0cddc2981eb913c39c9eaccd22e751 1c90c222ce666524a5cb01cc3d9e9296121922dc914a25c561f7290933ebc74a 406671c480652602f7dfa9d3028465e2cd79f110525b6446c622b160e1d9d8f6 d562965d08769b99a0349722131d68346a1afcfb0d215febe25d00a2d6e4bf6c b1ae3e830fa94f0786df933780168eebb7eb94f883be5b2865659f636d2d4503 3fb15b3c623e5b4fbe04641836c94352a84298955d711f48b854dc1d92975f1f e4594b5ab8ddc5fb36553978aa6ac4361329af00ed2fdc7c3197e335aa7b6989 514015f489d4493a0b53b8d4d632ce5cb31949338d197e6b09b49ffb934ddb6a 30f7c634f03e56097e55aad8da1f452347d8c7eb8eae4e9b9191fd30e4c8f8b8 a0e5273ad23aa6ec21ecd9667b993ee3de3118b943299bb3143c01cd34391f73 0db462a80e5ff0c5495b7adbb37e62134b75d28b28cc439a651b2dfae17b154d 948f61dff694cfc19a2b81fe15f566e83711898d422ab2da8d2fb27a8522bb60 2640549480b81b4fbb6599cce5c3a3313ccb7ce30f35956ea14965f292fd2c36 82075d3d625de18a7c7ac407b2b75be966e59f39aeb2129738f7598842a60f9d 31d9307e2ce9a6cff0fe88a1fb956298458c2eb709fd8328b57de03586814d68 edb536ce09dc34e13aeb3b5883dd501e4aee3ea7081246104443032f89ca9e71 dcee83be5d6fa85439b47b1a499358b0de1d1394be9f933fcc5abdbbcf078ce3 69ff4438e6a2cda2903489abd968066028a0d46e1cfd24b6801ad68966c0583f 0a78cce09c93fdfda0021c7c4ae9f494aa83e012a24fe03c5a76d5420f62e0d8 aa9d9407b35ac269ff49bebdd7c87a60e24f5fc1de355b3853097487e9ee2257 3aa1af60f6dc20c7435f4db72d15fd08433fe8d35197c327ca53cb8e7cff24ef 34e8 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY6 %!PS-AdobeFont-1.1: CMSY6 1.0 %%CreationDate: 1991 Aug 15 07:21:34 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put readonly def /FontBBox{-4 -948 1329 786}readonly def /UniqueXX 5000816 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bac8ced9b09a275ab231194ecf829352 05826f4e975dcecec72b2cf3a18899ccde1fd935d09d813b096cc6b83cdf4f23 b9a60db41f9976ac333263c908dcefcdbd4c8402ed00a36e7487634d089fd45a f4a38a56a4412c3b0baffaeb717bf0de9ffb7a8460bf475a6718b0c73c571145 d026957276530530a2fbefc6c8f059084178f5ab59e11b6a18979f258b8c6ed3 ccafbc21aca420c9c83eea371adc20e038b4d7b8ac303004b0aa205f04135140 76407216032fdd22e6219da8f16b28ca12524deb7bca073cc5eba65c102a5e85 fd48e6d062cd4283ee570a7774597e5bf0e3400b6be72db0115f3cb12db70ce0 83722870cddfadee715f10f1fcaf20e06f3c54afe5ca238539bfe2b596116e83 f5371ff18fa5003d8543226cfd4025f9940365b392a858d27f078d3abcffe4a1 54e78c7692d1a32bf935967c64f01b24788ff8325d61145e2d4a489fd986fb77 38e6b254522c77ca2797a504a9ce4676a77ebacb026eca94dde5922c936f8e90 c43e28519671e8def84a1526a8b89450ef2bd624857da91e7a4a832f89e4f9cc 36f6027a64831992e98b1707ddc56e562de9ad0278d89f3416dfab55ea0e5b25 9cfdc4787442890a5a8986bd394cfd87942f66b3712745aa18e52c6bd1d44d48 3f75ca3a5d39391f2bb9441314fbb25ed2b6813e66bbdec80f12a88c2f94f601 fdb6b48613c26c3ac738dcd4ab05a16c34aac07eb789901b095230281fc71f04 5ac83d60c6b82255c6276398134634a8135902a31a52e84b55aece4be46e9d93 72e8c2738a3ae29ce61298d5c2e792bc098a143f3f08614489 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY5 %!PS-AdobeFont-1.1: CMSY5 1.0 %%CreationDate: 1991 Aug 15 07:21:16 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY5) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY5 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 48 /prime put dup 49 /infinity put readonly def /FontBBox{21 -944 1448 791}readonly def /UniqueXX 5000815 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bac8ced9b09a275ab231194ecf829352 05826f4e975dcecec72b2cf3a18899ccde1fd935d09d813b096cc6b83cdf4f23 b9a60db41f9976ac333263c908dcefcdbd4c8402ed00a36e7487634d089fd45a f4a38a56a4412c3b0baffaeb717bf0de9ffb7a8460bf475a6718b0c73c571145 d026957276530530a2fbefc6c8f059084178f5ab59e11b6784decd2fb36dec8f 7478da853762e00bc9c52ba86ef50d222ff142abc18e4fb95b86b3e57d9390ca 86e8de6347bf7f48f93322a372c5d7830521b14e8fa0771961b027c81365426d d95d16b950e216a90f28ce806244ff28dd969cb512a23e05045e7b2bcaf7d6f0 ca8b51494f2ec0681bdfde60420628d9bce98a0ca1ecca9140f452a88db19a30 ed46ae881b098c843a51d06f9a153489357fd24de6a0c36cb5a9eb9b3b64dd75 18f83018ae7cefa1c12fd205df6880a705e28457af7b869a6dd28f6b37d82cc3 e51cba348dcdb34efb119b8ce5a996f15492b0f5d34538850a2c1b6a509fe5fa 015eceaf28b1f180a1f3bf1b8d488ac3150fc8c5a7cf9987b3d829d0de5efe4f 1c10570d63b8249375da09542b08bef2f71b347b8205709036a75c93c005ae59 00c917c7493923cc46a83273445c7577f4a80da26c5f135fac8bdaa53d0222af 2fbb21edf1a99c77e57efdef5ac21cf3ce7412683d79f279f4417e546d13df89 6f8e2d93cfebcacd743a35fd7a1812e508ba48256b3fb502a614745b05ef89a5 efbac8d3f5da21c163cf117400872957641b1819f3de9a42d2780ff05edff07f b68b7c2d3d62869a4bef767ccaef8244f9540a826e3443fd3d48c428dd09ea1c 0d4f1fe6a1376ef3d21ae242ba9e3093c4dcde237cf5efcfb56f09ac38eb9400 e12b6000b19fc1fe77c573e012c446835082511c6682d8364b8c52f6391fade0 3c5c6a2bdb9d43dd1f45f0599d35bebd4d726b4220a57c6754d53ace8193bcd4 07d5b626ddbec85bde18e9f943318f254c9cfe93e27b90c0e8a6cddb55df65cb 15f76eb68311b479e3a0c3b934817d0a0d12ea606202910b4c9837ce9a0185f4 0610a54e9d253f3562deaf4c44bea66e74abcf6498c6dab5203c8361ec94c0bf 4ebe00a659d4112d7a4fd42347fa56525d99afe90c56e5a0ab411998b1d83bad 8a0e14e4e7f9d99eee728043f72e732fdb90f4f5e615004fd20c99c65e6c4144 7c3cfd1116d7825a055dc1ba12 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: MSAM10 %!PS-AdobeFont-1.1: MSAM10 2.1 %%CreationDate: 1993 Sep 17 09:05:00 % Math Symbol fonts were designed by the American Mathematical Society. % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (2.1) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (MSAM10) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /MSAM10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 3 /square put dup 116 /fork put readonly def /FontBBox{8 -463 1331 1003}readonly def /UniqueXX 5031981 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d7190fa2d133a583138f76695558e7a e9348d37cac6651806d08527c1bb4a062a4835ac37784cc39ad8841404e438b4 d52d3901e47a1de4f7924e0fb3daf442499175bab1226edf692a4956739f8828 e80592f450c5d5c22ac88bcfbe9748f61d18243a16f4a4467f084e8e2be46ef4 7fc51c3a8199e3cda62ff9c4fb73956dab8b6683d2156377808cb35026073e80 523f59a30d195fcf9b9fce4ffafc6f33457e3200f0935ea98f1a0cfaff49cfa2 d877ff805620cba84126dfd175a82e1b4c6ec58461fce97cdd749a012e2c4243 86b199a97c306b282350cbe5af90cf1d8e7371dcaedbd5fa3346dd3e558072c5 fd51a2edfee6890f62efd1b552699123f4f52c2817dadd5ece30b3bc178a3ef4 f45fd8ad0ee5bf30db5f9eee9ddefe249f3c349a886cf9130cba68ae559ad719 c439930ece1d52d38366116c390cbeabb8fdb36811cf3b8e2416825e8c880b24 6521ec6880ebe7f127c8741c756b29e1f89e3fd5d638a7bbade8c3a0fdbbf7ba ec37cd372afb2d9dd25d509726d20a05914e418f6b7e759c440beb61519df02a 06734ec1226890d17c51f25f775e6879fdc231bc4d7fcb4b33d04fa273bdb8e8 f124171714614f8a94e98a6c2d6bdc1254913999f9c181e42c0886556cdf48af 92a265c1eb06bb30fb2745840c17bd31c7b8bdfd37dfb9643a418a2eaae14094 6752e0a315207aef85c3c2630538907971ec1b05687208571a3504bb3369b5c8 9a43e5abe343d0599fd8d41a1bf01de49f5856bdd67d63a2b3ecea75d721a6ca 0c8751ab41e892e9cf674218dd44acfd40019bf59f4d69ea40d5cf9068a6ff96 9f8cc772b920baf17334833d732431a2969b9a30fe38bd44772cef653935a957 af61dd568f041847ccce3c587656cba7bbf46d8cefec936c6d34dbe51bc04929 0440354f3b29ed8e6b4f21ad53b5809779d67339f284563d54ed4d2a504b014d 974a31c0ceb57b364af519bad4e85c41d521a3ffc26dbac555b42dc191367152 1d60c30b95b5bbafb3c7d87a1c043ea5f0e6dab83a4de99a742e75f02837b923 c50eb478ac4131ee604e3d7b784bd8c93eb9430291d452c21be0495718546333 66a602a9f142a563fdae3c8d40de6a8aa4f3118e6b59bd7a2c35420557fc465c b2c852523436519025d7013ec029f4a3b529c171ec5c6d5a8a188b741f64cdfc f531dc0d5851f9d620c3d30c2d1c7f1b71b47acee7a580d5c2e7c58ab08d5af3 41b5710ac3169e524799e662da50cc19ff2eab91706fe0ed7a96b80e0c9c4353 21f163df55c38ef810171ac098fd8b63fd068bb2d464bb84f1eddb45dacee878 d740c732de8196a72717ebaf4348af2c9dbaf34433299464d4959a4880f79102 868023d179b3d4498775adf1cdee25966a2f3c2f953dd19f8b48d1f69500579d 858b8118840ee4663e2caa7dbd68b855e423341dac97b7bfc8f168ba099ce9ab 45aba4386d1ed2b68edad6465efa6e3cce07f5cbe586624dbc2a97cd248de2ca 4002b6582ebaf0650b7ff0cab015c3e031cd7b4394bbb1bb4a57d74556a91a45 b9051f82857cf67dca6b805583fbc049e7db890aaccbbf6a0e6291a031bdf124 f6e230f585667ee45783f3aa81126500930dfe64ab3cd80c18d9b408a425dec6 9be2b289da675e1747a811beba8af60648ec5232089350889574a4d0b14cd4a4 fec84a689ffe63ad72fcd4 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI6 %!PS-AdobeFont-1.1: CMMI6 1.100 %%CreationDate: 1996 Jul 23 07:53:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 105 /i put dup 106 /j put dup 114 /r put readonly def /FontBBox{11 -250 1241 750}readonly def /UniqueXX 5087381 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d725e830d1c76fba12e12486e989c98 74c2b527f0925722787027f44470d484262c360cdfdddf3657533a57bb16f730 48bfbbfcb73a650484015441fdc837add94ac8fbd2022e3ec8f115d4b4bb7b7f 15388f22cc6198efe768bd9fceb3446ee4a8dc27d6cd152485384ef5f59381ff da43f2d20c8fb08aa27ab2015b774db10dacfdcd33e60f178c461553146ab427 bdd7da12534ba078ad3d780414930e72218b3075925ce1192f11fc8530fcd5e3 038e3a6a6db2dcfbae3b4653e7e02730314e02b54a1e296d2bef8a79411d9225 dad7b4e6d6f9cf0688b69ba21193bf1495807e7a1e67ed7e41cc25acc04702f6 8ef703e3d45722c1a91fdef7100a48631a02a6f02a08c6b1f9b4df8310385b86 8632718fd87119a233f219d9411383b7fa9f3e4780d8c27e2e89e0cae883d664 c3eac57a3aef8988a2e9f0f8c7f53e0a80bdfc4620e21287d0390e1975398544 7f3ea66401024bea75e1b4c4437b7bb188f76f96b918ac7c6ad7e8ae7f21d8c2 790f08cccec904fe48ef39e597ed4d4237c1d1f596f5906b19ea308020f7a35c 168e327ec3246b1dfabe912f6b6daac09974876d3996e57d180261110db05f15 e3e8eebba3d90b5764c03df3033a1ed678ebc679569a2fb297378b25434c0f20 5313ecb8a952f07242d3ee731b0cdc086a4481178a3d65129c47c09b22e9c431 e11b3747b94c26a757c38d06001798c6a568303d541385244b967d3b1786edea f65bb53c4c2fe75e4b1b15c2c78d930b4296c80f08bad86012451edc8e9f0854 c3b390a16e27b11b3d45a9f72eff8baded2242dc928a61685d79e09681c97425 5b90a498614cf560fa5b1718981388268ba206a96989e6d0b5d485d9aca5594a e67dd7b34d8a369adb06647f8aff8814d6d9cdc04a4835918e557174c5bc0f3f bcea9907a04cf93c12727ec40db3f2f77596dca477862747435bdedacd9b2311 6cc97fa47ffdd7d897fb6bdd5572e35d34e7e1cb5e7273a4ffd86525323ace4a 84e1297028c2bd5469baa2e75d19360c2c9042139d5e7dd4390a6a3935424711 de21910126d750ae279916ceb71da3591d60dc62db333c5021e2c1cd61ade51e 93971def6fc0aed1bcd3e15825f528f4afa81d643833b721f031f44803d15d08 d8b886f668cb29fa77e4e321ac9e10ca4884aed02890fb355d0b250ca7e5bc46 700aa8ac2699791a8caffc7e1fffe11dd7794fd811efa0fa67f1788952ad9272 f3b9bcafc560af96d302eb79e178d9a72b7f1bb567f2311338cd845302cfb9ba 9e53fa81b7520dd851ddfe3edeb5cc755c8c1e2bf42644399904a20e03c14318 97cd201614059c4d4c7d99f85ab0fde9fa1e7bd7051fcf3134ebb4d6bca229f4 f21bdcc2d9ad2432f1bf0e8cb4c5ec75cfd3175d4b707e1a21b0683a23992e67 c7d141e389590d7305417422436528de43c90456de24f30e4973af5c41fd0b4d c27ce9f0d16abfd3b41c90ab0c8c161ccd4f345f66393fb3b4af2f0b0c7d154d b0d2ec991f3ac93f9d93635158d4f1c4be59e831262b5f48bc67b52d4cbb3ed3 6a21de0cb1a46857c10a68b1ef997819a5ba7198e99ad221cc0eb78a4d0a1213 9130cf43a42157c536fe6fa03fe54840c5e741f9fff88a35110627a25d178f1f 2961c57e020d2752fb06179c70d2e8a5e43992048f358c00879c9a6bc0474f0d 9fce65c9550ab6cb895f7e7e12bee4bfcd1e101da43395f5d459ba0bcf23de6e 80e5d01d04a798132b12bcd4274c3e98a79611506a387da552c2a4433915ab23 36261dce8d7a5c6eff0383afb88242e2393e3d63b5ef3d05cdc43a2a9ea8fa46 116e46157e7fae198eb58f8c451d69dd859adae660789465ccde80a33cad6a02 f0ca68d12584f9eb12def6c6134b2b07d07701be502bc73c6416e38d7628716f 69863bda5355b7e9fc38dd2c8bbe14b33d8a7be2b7355d8b69cf15f2e16038b5 e54955cc346d7cafb9bdfac75d5747e1ef1566c994d335998f61edfee2346fb2 134e57eba3a339019640bb33365fcae944533c98b3b6b19bec9ceab30adc5ea3 5543efe8d8039ffac94927ab4ada43f0c3e0d31a9fda61f37c3089882abac49a d53fd0492a46876613e7f2a27463ac1b2b629e55f8583fc099c1de 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI7 %!PS-AdobeFont-1.1: CMMI7 1.100 %%CreationDate: 1996 Jul 23 07:53:53 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /alpha put dup 18 /theta put dup 22 /mu put dup 23 /nu put dup 25 /pi put dup 33 /omega put dup 34 /epsilon put dup 36 /pi1 put dup 58 /period put dup 59 /comma put dup 60 /less put dup 61 /slash put dup 64 /partialdiff put dup 68 /D put dup 69 /E put dup 75 /K put dup 76 /L put dup 78 /N put dup 82 /R put dup 84 /T put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 120 /x put dup 121 /y put readonly def /FontBBox{0 -250 1171 750}readonly def /UniqueXX 5087382 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d725e830d1c76fba12e12486e989c98 74c2b527f0925722787027f44470d484262c360cdfdddf3657533a57bb16f730 48bfbbfcb73a650484015441fdc837add94ac8fbd2022e3ec8f115d4b4bb7b7f 15388f22cc6198efe768bd9fceb3446ee4a8dc27d6cd152485384ef5f59381ff da43f2d20c8fb08aa27ab2015b774db10dacfdcd33e60f178c461553146ab427 bdd7da12534ba078ad3d780414930f01bdaae649990604a33aa9eaffbe5b5489 e5c7c9ff9d9be01b08220832c41caac64816b53bbc087ae4b621d2b44b21ae5e 3f7fe4ddb05c675abfe30510eee4a7c874bb57b2ffe521a6875eddfdfd18c781 25bfca5a097aad361dd94df46f14026c25ea988194899b95001209cb7009cead 4b4ea03473ea120e7a7e341d4e3926796347fdb3a124c29660ac09f4648b313c b58e824884382f24ce08d2edc686923acace1201c16a07a42803288cd0b946f7 546510e95b1fa1cc96f0bf72aa823d8e83d7c68c752c82a54c752eed2b1e699d e9db1830272ffbf2f4996ccc2d6fe2ae272798989525ef3b67b0d09bffcef749 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1158db9b849008fdba349491b308cb94ed6b5b57b1411e564a24d28fd3f4899e c4be42ae0bd6bef70ff2ecb02fa9d446513d6868814cdc1ace262d0db583f80a 34977cce940769d027ab7d8e6981757ef2501b55cc984962b4f8161466c3d7a6 310cb152e5360ec825a57ac001cc58bb5c25a0965fdefd7d4bc7d405e72843bd 3f230ae538db8845e6d0420860ea7e39b262923f2c29218c324ad56cf9684840 e93581b5f18dd7c3e84b1ed0997fd1443e50e1ced154bb9cd68fdd2a49046033 2c108c1c7a7ab6acff1d9427c1b953ba74dd84e254e7651881dd762782f535a2 55586380291a4ce8a195568c3b0b44facc7c0667107fc265db40586fad66e9a1 bb712cf35398a6c0e7748a12c5f1937b536095d7ed93c369518a78969ae7c1d3 2b7de4e6a35c330bb2a812583c05d3bf4499b6770095be0166bf8820b17669b0 7cfb165e5a41dd4967a19db2102b3fbb43f4fcba7d2f9b624cbd53f7e53a357f 8128e29adb08610791b23a9f9667a3a703eafd1a283f577d0638e95dac08f965 7c988d17b706087e673f1b904aeea43c0deba78e7ee92dad7d0b45e931fa78a7 d1fae180da415b17535f95f1e038d773485f71f19439302f3227cad4c0531aa3 a04e618fe2336cd1a247caff01fe16a84e51663a79508516cb25cb0e68da6728 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68e83fd1c55c5a329f6c40f82db3b81e486a3bb271c14eb8ca5335fb76c17c85 99415aae9b3477b6b88c2248bfafe484777d7c6f4659a005b3744dd76118f903 4e53c50e659b453f7f8584edf0ada9b7034d76a0a4a484f84d76ad2079d23645 74d24038d324aaba65b95e89452d7464633ab8077710a00bd93050efc02cf2e4 ad70558703e0e45a94751f6430a34e64b274e59fd3847e893f7298f4315038b7 9d05bae3cc2dfa6392d67fe8d7592f40d296d6b03a44815334297727a3291487 e78d839b5b489787a63055d7d251471b88e352256dcac9febcaa1273101c63b2 77f9f4b3a57e2cdd13505cd61c6ba24104871eb2d048a948738c7bbed8f438ef 3d34c198486f71ebebe3621eeab61b9d3589bf8304a6bb0bd27797a6896fa007 8d21711f5f5e884f1e43fe29bb43732e950c30505f59b8922889dde1df341bd3 ffaae980cc564910b9bab96904ec669e923e0334cbec7bc91abffb9bdb26562a c1d73d1621eb216c016b28e2a1deae91092b94d1149f2326ea0a9b021d28efda 7996ad57ecfaa0ce526f77f4e20e9bbf1c1d6cbc8653ed52edcd5c31d2e8c817 dab4be5df01d7bfc4ab642636adf0c5166d07fb655e095b7382894b74639b0aa 5c1180f5d13c1c21d47e7a78a9fec9d7519ef35443d6966b9b95071fbd3d1463 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%!PS-AdobeFont-1.1: CMBX10 1.00B %%CreationDate: 1992 Feb 19 19:54:06 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMBX10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /ff put dup 12 /fi put dup 46 /period put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 58 /colon put dup 65 /A put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 81 /Q put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 89 /Y put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 103 /g put dup 104 /h put dup 105 /i put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 119 /w put dup 120 /x put dup 121 /y put readonly def /FontBBox{-301 -250 1164 946}readonly def /UniqueXX 5000768 def currentdict end currentfile eexec 8053514d28ec28da1630165fab262882d3fca78881823c5537fe6c3dda8ee5b8 97e17cb027f5c73fdbb56b0a7c25fc3512b55fe8f3acfbffcc7f4a382d8299cc 8fd37d3cea49dabdca92847af0560b404ef71134b0f3d99934fc9d0b4e602011 b9cfb856c23f958f3c5a2fbe0ef8587d1f5774879c324e51fcb22888b74f2415 50d7401eb990d4f3a7af635198422283cac1b6cd446ddbcbd915db9bff88844e 784c6bf7389803d9450b0c21756a017306462c563d51ece66fcc9c831843ecae 1fefc1a232e2724f7baee428ae03aadb95c3035345c15e9922fe49e1f2cfc980 237316572dbc57064edac9b0db8913a5e2d45e97e19a91435ccf8adfc835b585 48e74b291446d689c7f2f8c4325e8356e974ae30c3e2977477baeaa33d141fb7 80f59351e84bfc88c87b3a4a1d25e168b9d134554f6a581378c7d2d6eca8ac09 045cc3a5e0ed86f147133f094029e3483bebc81cfde69942cf645ea20d0a2b64 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7265b93b14ae9abdf39843e96ae6be12f6f44ae64f2086e434e85b169ddc6031 e82b29fb149efd82e692f6f6469d56f85f49ae284b31ccc5729c4c86e5cdf7b7 a447ac1700be73330ff94453f93fe153e8d85093323248597a4afbb8a3215ff2 e82c09116a67acd257339b6ef02e7335f6f32998c2fd7ac74db499b3699c9861 2a81bbbe8233743c9c4a0314058dfdc5217fbc377022753f29664038fb005baf 822b14ac43a74d8e9a3c872b4b6812b5a3766561 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI5 %!PS-AdobeFont-1.1: CMMI5 1.100 %%CreationDate: 1996 Aug 02 08:21:10 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI5) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI5 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 23 /nu put dup 25 /pi put dup 33 /omega put dup 78 /N put dup 105 /i put dup 106 /j put dup 107 /k put dup 109 /m put dup 110 /n put dup 114 /r put dup 121 /y put readonly def /FontBBox{37 -250 1349 750}readonly def /UniqueXX 5087380 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311e252234d51741e18db3a68e8ad10242 29e5817a10e796a78d2c7f7c1f50961b9a57aa604c9f821dbf5a9295197bc666 31678d7d2c7e1f8f2151ce0c29efce46270570f4301c5dad1b38884732e53dad 05dfc36b020e726ca575f71f04abf2b49e1f1d6d2a08a477658ca9a48f1c8cce 14382f0a42201de56e2821ee2b0e91a818b1b753d810ec2428dae5153b66af66 9442192024becf743a8f6264a58a0b3aa823510a4957d1bab3e1b83135362888 3e392f49926471a8021fdb48637baf0abcf31204b1b214f48c99f44af7782323 69d772ae4f49be53a1bf584747bf29b94f530d59a5be5370b8dd0691e32a21ba 9d0d592cf3bb50a99a3ecd18d6c4114cb4cfecc49705da90d7edb10e3a28f9eb a49347a09d31eec896f2a28e9607d99d42914aea16545c16e136bdd0b75fe486 61e24c7a9e9b233a76754c760822d0a88c575e08ae3e3f081d7bfb80ec4c03ac a08b65fb6474f71fc95c7c2462f2eb3754e647c29498288f2ced0bd3a2bca5c3 2f80a61fa667802d376cacd34de1f9572d1b3ab09d6f352750db4a768f869638 a87457889aa502850427b40e1294c5ba33e6b17532b2d13b5f50e71582f93daa 231e86597872a2a968127afb0f36257a76ce1eb24e6c4f29fce2aaf6532fb5cf df84da03f03a45b915209f67d398c7c4f7a3b0623750259087a478dca684b29e a8b7f52060bae9394369ed1cecc645d113cca3772a8dc36c6d916b5c5e65454c 0a188a33395fd3da67ad0a31ddab6a8434dd80f0bd0ea1a2a62eecc331d88b3e 369552daa1c575a98fe84383548626b65be7c24ae7eb61159f149872cfd87cf7 6c1a7c155c7186c7600e58cb61b8cb0c5dea98268a39e928bf6fc53985eaa763 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29f9f80296b0d3c2e5ddcfc2432939ab21cea196808e26a5cfacd3a21500d3a9 81cc10e414fbedbb96fefabcda773d9546ae71d3f8d33c6750d5548db27feff1 7c009953458364365456eecc9c1ce99a2b40f5cbac0ca49242dcb1628a805f83 d7642cf1fb7be85b4aef98ff04e2a3b1e1efc236130ee3ea7d1b04bf6e9ff227 93a74074ba72ca82fe7f280c75fbd985c71928bf2ea7691f6ced2f19b3f4d3c5 54af978f8b3ff795b2440aef9257fb37022cec21ae29710ef5ec8be11d391d9d 9c5d1ebb11e8d9f13a13492f5c4c60f013344cf0ded750827f0d460150e4766f ef4256084294926fc0214dbe106b8ba68655a50553405cfe26e6146beb2f7fe4 33771da43d2313f704a03b25551533fbeb08d0f0799c202966b5ca4c61c29d56 77ff6c88825fb2eb18a94c44fef48dee7b6e697395939cdc6371dffe2ce79096 120a18a8a1a521d79ccdf6390f417db0abc7b92100e53005504ea78d815a0e64 b11c1208b1a1376857e69646fec0038dd7806e7014e783c02a4eba935cd3ea26 7fc6e3ea13942c0d25afcd33e98939850f5c3aa96b977c6939b1ea583e57face ebd795da8cf5604b3c0e2a2fd8abb5d20214e1324f961617cca9e92027fb5447 ea12c8ee1360ea496bc76a0380aaac84f2c2bf859a274da982eb113f72e7f592 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9cb201cd8ace08481990edaa851c7531ffa581b6daaed3dc586fa3c7571076d5 a6a0956d6fd2b27592a2ed5378dc557a1b66d2529e145612b7e18552eeed3c6f 87aca247e48b6294287f045d8b06d6dd82bd695fbe9793269e9cd7393c595f5f 27de7b4fab16d3fe909cbe7af35466fb8b788df9ec74c3cbc0d313984f35a379 f75b9240767df479dfd5f97b22bdd3d1a4d290a2111fc96ca13c9a613561af4e dbe5d1dd33bb08db0df1f31b945ae11f57d36ba464bbcbc18c93abdee5c5af98 120e025988772456b1df6610408b10c60aaf35b52e1e7c6ae508cd431f019e22 dff97355016eedb52e811884e63ef8785cf38e5cecbbf7de20f38af645d12657 73b67049e8c0d878d1ffe8d74b9845d1f756cd2c266a2e9b411fec603639cdcb df7cacbe9bedc9bb98a527b3f9c4739d7eee5a30ea57b6676857ab460461edc9 148417aa46cf29fdccabce446d72c38fcd29eb36af0b8c0891e10c0338244f47 d900d8fc95555dc1094ca2d50d16520aa4724e4abcb0989f1fef7cb73ce495dc 2ff813cdf66292959be35e9aebc69cabc24b8881efa53780d4b96dc0def80482 aefbffd08f6006a4737418dee1ea9de03e62c7f141fab6d75d9c0d0a41dcbf6e 9427060048d943c96f68a68324 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR5 %!PS-AdobeFont-1.1: CMR5 1.00B %%CreationDate: 1992 Feb 19 19:55:02 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR5) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR5 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 40 /parenleft put dup 41 /parenright put dup 43 /plus put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 97 /a put dup 105 /i put dup 109 /m put dup 110 /n put dup 120 /x put readonly def /FontBBox{-341 -250 1304 965}readonly def /UniqueXX 5000788 def currentdict end currentfile eexec 8053514d28ec28da1630165fab262882d3fca78881823c5537fe6c3dda8ee5b8 97e17cb027f5c73fdbb56b0a7c25fc3512b55fe8f3acfbffcc7f4a382d8299cc 8fd37d3cea49dabdca92847af0560b404ef71134b0f3d99934fc9d0b4e602011 b9cfb856c23f958f3c5a2fbe0ef8587d1f5774879c324e51fcb22888b74f2415 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521dda008cb7a2a77fe4eef155af4be51dec6ab61f1d83de666586e426a25b5d 96bf16 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMEX10 %!PS-AdobeFont-1.1: CMEX10 1.00 %%CreationDate: 1992 Jul 23 21:22:48 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMEX10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMEX10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /parenleftbig put dup 1 /parenrightbig put dup 12 /vextendsingle put dup 16 /parenleftBig put dup 17 /parenrightBig put dup 18 /parenleftbigg put dup 19 /parenrightbigg put dup 32 /parenleftBigg put dup 33 /parenrightBigg put dup 40 /braceleftBigg put dup 41 /bracerightBigg put dup 56 /bracelefttp put dup 58 /braceleftbt put dup 60 /braceleftmid put dup 88 /summationdisplay put dup 90 /integraldisplay put dup 91 /uniondisplay put dup 98 /hatwide put dup 99 /hatwider put readonly def /FontBBox{-24 -2960 1454 772}readonly def /UniqueXX 5000774 def currentdict end currentfile eexec 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3c65acfed040262fa0dd74d1d9283901ed00bb524abcc37c8cbad74f58235e04 386d9bc548740708cc605412db44d6c31cca72 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY7 %!PS-AdobeFont-1.1: CMSY7 1.0 %%CreationDate: 1991 Aug 15 07:21:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 3 /asteriskmath put dup 33 /arrowright put dup 48 /prime put dup 49 /infinity put dup 50 /element put dup 106 /bar put dup 112 /radical put readonly def /FontBBox{-15 -951 1252 782}readonly def /UniqueXX 5000817 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bac8ced9b09a275ab231194ecf829352 05826f4e975dcecec72b2cf3a18899ccde1fd935d09d813b096cc6b83cdf4f23 b9a60db41f9976ac333263c908dcefcdbd4c8402ed00a36e7487634d089fd45a f4a38a56a4412c3b0baffaeb717bf0de9ffb7a8460bf475a6718b0c73c571145 d026957276530530a2fbefc6c8f73e9b697ddc0351763500e23c4d170ea8a2d2 75ad0b6b23097f02fa803c1f46f9ac10fe0e527c431b11b1b9a50e874896cca6 17fe3e255960846bc319ca68b9b930a45d5d0fc36b352c3443ab6f7793b38d2c 7fb9c409ab7980ead55e9f8f6b83c70088d1fa6d7f2214da8928e40b96334ad2 72d1b5db9d1355a579b26a8dac21f021e393d7d837a95deb8de92ed818a8b80b 98ee9cdd8a3c57ad7d6eb7a82f43eaa6ec520eefa7302e750edc4b495f70bba2 24a2182eec37f1a1c5dc8e20973007150237daa6bf03d498826777eeebe09014 ebfe05a8731e1a421cfc513d47d673e3d94d805f5d0668ffa265e0962cb5a75a 4a93d9b879a7461a1778eb031b8e78f05debf78995e46bdec6fc8e97a438f17e 5768f7a375209ed72b01e2da4c4f8a622055286248fcd77a96c07d0eb0ace7b8 cb27c92e61f35e672dc3b9011111d243ec69c7cd5030cb5cde1dd8e308a3ee06 cefe87aa7858f84c256d9c54c0d4e2dfc75c3edcb35664ebc662eea98cee5766 4e5edbc056098b07f8c7654f499594819f63973ddcc768e454149fe10f24ba85 916df5b6929f41d46dd0ef919fc13ff95b1a0a8e59d600cf5fae373e9e5eea55 421e2a1d29065a31ab0a1f0a1907a99824f59d14bfd7784bfececfac2cb060c1 50ef01d3b4d086948e21ccdab15bc802f3921932b3001b5f57ae3ef90c8de647 cacdc41bbfa4ebaadcf1e609fe6dea44b93376a56518e3108927ec0002ccab41 8c8a3cab17032d33072a63840086d4e2a9289d97d327f702493a42421085fc98 add4660c101db4d6313e1969ae70327221b1476eacf28f821feca1dcffc643f6 bf73cf62645f88c725a75cce23ea5638e47d88d6561b26aa79d1605ffe587120 ae88032c55449225a566eacc4365552a959836f9fc33c0ef82d7a75be02b43a6 a01eec3c576dd7d5589ee53b3af390cb18cb1f559096fba22725d2ac5dcd2c15 8fe3cbff1077b90b98fdbbd4689525e5ba514f9d06131f8b4146c88d6463a4b1 b6dd26130ef258f1c14fe2791f034a3f41c46fa5a20158d344dc542ca548f13d 42dcf6540cc7d817293caff839235fa60a6348194138c784c54af6cfd5c5d6d5 21e9f022a8892e2eb1876402b608fbe31cc625260a2cee717c9eb4c5c72e9957 c0ec43c306030074aba75d6faad2122d223a7b05944a11e937d787c0e79e91d0 e6bae1767f53815b8b590f4891a7b12d3b6657ae6770e6eb123007ed5addde8d b42af026e359f721a27ecd41b091555f75177b2225f430f49f9b5931160aeb49 4f0499b4039aafbcbfa89aabb3b6522327f9eaf1cbcd901b99f9e07f4c20a302 6fc34e9aa83ec310bdd2fb7062e3a3c62788eb614438f8ba78a2fcd9ff1a7f7d 13645eb419d9ccd7cb504b6824c6aa9f2064bd3dac004cc6ca7255630f0ff960 a0e464a5e7b377f218053394c2768ac45ce49b904d49859c90bba92818fa1050 4e4233ebae58e69c8b90695bc6dc1a25e57990cd868c088a49876f76dd3a2409 dc19d20129ff9eebaca65c34d60541f947d1ed42b298b6e803a0ebc0fdf05ea5 d7023a18ab70282e3417db98da1295c58728cd1c42084647510760a70d94f43f 08eb45054d4f373222dd8eb9be3f0451febea6e424947a5a5349c2ae6a580a05 35091423c30a0c3ee1911e635ae5e26411290204236f507f2f9ba506df4ec8c3 ce132f2f68f99aca3bdf4a4b91c70aea55f19bc45c42716dbc576e02ef383fa9 52e1a553a51eed66764b32777f128430794ade4583197e5e3beaf47754e0cd66 2f25ac3e5ac137f335e7525b4ac732b3a82e35a865e96e7b97eae257951add3a 9464f5bd4e34253aa4b1c03c68fc7c094333e22609ddf800dba79848b2768b59 239a6cd2cb2569d094c885f8f54d0916963415d4c9d1195d91e1be7b90bbe81a 232f42a4d045c4aa913e2262a997e37e4c95a05c0b339e78208d8c84a6da006d 2ebc5343738a7702cfbee6c5d26d330749f030694a10 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY10 %!PS-AdobeFont-1.1: CMSY10 1.0 %%CreationDate: 1991 Aug 15 07:20:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 1 /periodcentered put dup 6 /plusminus put dup 15 /bullet put dup 17 /equivalence put dup 20 /lessequal put dup 21 /greaterequal put dup 25 /approxequal put dup 26 /propersubset put dup 28 /lessmuch put dup 33 /arrowright put dup 49 /infinity put dup 50 /element put dup 54 /negationslash put dup 59 /emptyset put dup 91 /union put dup 92 /intersection put dup 93 /unionmulti put dup 102 /braceleft put dup 103 /braceright put dup 106 /bar put dup 110 /backslash put dup 112 /radical put readonly def /FontBBox{-29 -960 1116 775}readonly def /UniqueXX 5000820 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bac8ced9b09a275ab231194ecf829352 05826f4e975dcecec72b2cf3a18899ccde1fd935d09d813b096cc6b83cdf4f23 b9a60db41f9976ac333263c908dcefcdbd4c8402ed00a36e7487634d089fd45a f4a38a56a4412c3b0baffaeb717bf0de9ffb7a8460bf475a6718b0c73c571145 d026957276530530a2fbefc6c8f67052788e6703bb5ee49533870bca1f113ad8 3750d597b842d8d96c423ba1273ddd32f3a54a912a443fcd44f7c3a6fe3956b0 aa1e784aaec6fce08dae0c76da9d0a3eba57b98a6233d9e9f0c3f00fcc6b2c6a 9ba23af389e6dfff4efec3de05d6276c6be417703ce508377f25960ef4ed83b4 9b01b873f3a639ce00f356229b6477a081933fef3bb80e2b9dffa7f75567b1fa 4d739b772f8d674e567534c6c5bbf1cf615372be20b18472f7aa58be8c216dbd df81cc0a86b6d8318ca68fe22c8af13b54d7576fe4ca5a7af9005ea5cc4edb79 c0ab668e4fec4b7f5a9eb5f0e4c088cd818ecc4feb4b40ec8bd2981bf2336074 b64c4301d7f369060b11254fa45fa0af71e1f183cf8064451f314ff167564da5 1dfeca1ad7fe404ae36de12a89be6361e68fd4f546b462d0acd9fa0ff06682df c9f38abdd9812ab83bb6e040e7e4581583b85e4c6d9f5360c2b85e0fe4d1d2f3 6093b7e8717f29c9183246e8d679ffd5cad4434cbd1aacfc914ee686c160ff3a b9fcc35dc7ca229bc8b23062703eee33c65eae74a2c188b28e40092657b0f8e7 b153b41c7eb04ce74b1dddf49c5e6cf579964b483350ae16bef13fc0a19506bc d74f30375c34c0db30e67bac8079fba2edd7b4a7a493bc8fa7c0011106414262 5e4724d80def824b99316f55bd40d3d0f76683cfec3d3de472d33d085a704c45 c74ddda559e94881ddca1f50e163cda9b1f2272ad74fc0754196f3156b52d131 611a45fbe1245e65b8c2f82f1daf24a218279f0adfc64a6ee6969c1a4b559c9f 680626713d9d5d7483591b40583df5d3d31ea8fee7c0d31063db6c29f7517dce 7a85ed940341bbd11c24fc72d1f7c1e42f1a3558806fa568f0c6584f3382481e 4417079d4a70c7f263ae6d791ba3403e3a296679a49f644ab50505a1ebc29189 682af0fc8feaf77b2f01dd350b5d2d129a5806e0ccae6be9a2b5a965bb95a34c 1c032490f87fa656e3bb613a84404cb5a7766ddf599346c62366aea21e2e95a5 9939269b964811c3be1df11319be175259609c03852967ecfc743b94db8f6cd1 0ae44831eb4dcd36ef27a9d8aed0e5f1d0334f483dc11ee613bf97f1ca95637c cd98b69722bd940b6c1c4a451b36f5cb8816b39b34da9914dc68e6223c7a9fb2 2038df1be1227461041ee274a6f857deef30adaaaaf9f8e3fd93bfe7f54c1e9c 0b123510f3ba34c86e55ea740258855d962ba8d2f4e0d15438bd7d94280e2af9 f8868ab2af80cc2daf76e6e019baba975fb91fb189b0f066b80fe1acd2b3cf08 e79b6afa6b31e08eb9c6f2357fb395fd9b46e9cee848dd64731e37884a7a7eed df7d8b4685935d6b525406ab2ebcfc5f49ed0f9e7c4cfef6f84a2171afad23d5 a9ac7e22ec0431009da9949b7de1bc4c90b56be0f763bdfe27f15a21f13f5848 821b7696a44e9d1a1b2e0347f2ff70b22c8b734acb734b69b7ce248877a18934 4dbe2449e47e531b7a75fc8bd07845a8a8dc0ec18eb4ca5b2210e9a3765ae4c7 d4d3de4203edfeddf192f43110edce6a5c85d4c7ce4e5119af0ad36e4bf95c5f 286b2fb896207fb8202086f58c5c157954bf7541baff83db5c7a7714a2ef7186 11f665fc21903e17d7cfc3ee5b307e7625b2bfdc4b836e2a82f62a8433d5f2a6 ecbc9fba15a2fd3b116fb396d31408674372ebbdae591bc8458718a5c53a7e57 0e24c67cad69b3ad5939f8383730afbc254af51d50bb46873db0911b75d21962 a73fa7ca1e0e508dc5b190257e0099d80e601264cd549934f937dd5d3eeef3ba 576ebace6aa8509b4ef8ef62e9ed635b9e9ff9d28da81b66dda3879cf252346c 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54941a149c66fa075162302bfcfb9d6c7434075af9429bd60359e5e5eac1b433 9c0712fd325d1bb865618b993dc2b2e580999c60d5c14f8042f0b81fb43480de a6405fd34913bd49d8ef6b32dbb24231406b7f36d2c1e7d89b566bf5794a29fc 8d2541315db5d0b7ec9171320f8ac9af46c42055c7baa3f632ead1dd093b6496 e4178eda760ca1106d0473cd673dcb3141d3affc4af6461f5d2080bfec7f1a1e 54f1f8c3f8298270596869f90af13a2829ee2635c2274bfe840b11ca2270c5a8 1c7eb043158a9aa4c5281b72f5b263d55d91474e6b1603c191e8e8393edc891c ff4afd2ec26a030126652b88a872026fb006e6d363c7290e379469b85b8ce15a 91e874485b7699c652f3d65d6738f67109b402f9c269a348284acd53b4a8f6d3 dd326997d3ca916435e1ea3e5991d318186aa0d15544d2957185e2cbb9f8465d 1524e00ff03eef04ecb632e550db8a4e75193f82e68953bda3401f9dbf844472 73a38d425938d3e8a1fa942a3d0925f8f314ecae8689b48777b27d1571815857 efc348ec4074c0dd328b729a682b1e9f71efc2e46ccee23f515af77e2414851d 5ea79fc504104efd474ae4f6663a443cfb31405728fc5dca29a8db58fcfd2a7d ba880a8e21fc76fd944976b79a7da2216c13c4deee4be8ecd76f24ba460e74ee c3f4ceb3b2b4b65c31ac1a814c91252a600d92329f83984d300fba243236d206 10e52d1e2f94d4bb80f18109dc35f64d5baad8d081f0ac70580b411ae7ee2a23 e3a93766f921f87cf933ff7ac1504a7d3ba418faf385564e12144af875ac1fbd 3de2b0e4fe26b5b088460179240aa1447f0a868c60a6c06b70f9eb170dc75924 9ccccc43ec735161fa00c7d906a29aceb2fc25b2d8f5270b1b094c776144394f 43b4a97b7aa5908112915b161b5b5777f53b580ef0b45be7804734ee7574a8e9 b7420fc68bbf29ca0c896377d11f581471438862c4bb12628433eb1020aa069e b912deeafc9d2906a634d5548066bca2b28da398bea3407fc4f2f750304d6f44 78be642905bfd08fa0f2380125692afb14761b77b2addd1d59ae5e19e4687e96 bf7df5d5cd63aad4125394940146f62daa54ff3f3a0930a2d8a92134d2e2432b 2bf2d6223977043301190466c5b7aead9827e7e8abf1e629eaa1dbfa794a12d1 a4a7d6dbad36e54c3159ee93f138e6c7de8cdb9c595f92b6e24b676774c781c5 d954896ae3e0e67bba2949804a12097f96eb1d7489188b7d057a9f42d6b17f12 f615337700825fe0de86d11ebd404b28feba30d1d9a607b34b571b5657c31d96 6ab8859c30772f52a1dee482a0b0e0368840fb8bf31c856b8ff497b6a3e601be fa8feb052d2ec909e1485d94d16508b73f8bdcced1862e3aada94efa9a699740 ac9b8973ceb5c7d0ad640a25d79ea216d154a52eb8d57a158ab44d5d6288845e 4f0e71a0e55b71a1c75f46289b2108cda8050d6d80b58fc003429dbcf3b19866 87135769a76f5cdcbce5c6d5578a7fb66f4e4b9b87c5d67ac8c5679d2f70ba73 7bc648cf7562bb62d8abf9b323ae48d5becf8803bf7187e8dd120fb8f34b89c9 1747ecb244628140d437f2ede11f5add241dae60068681a0c9327fb458ba3358 1b4817d544dea0667971cc5511e861eadddc1e8cf339ebd6316f0092629b30d5 d80550a41b7c9f8f3e42edb500cfbcf25901b37f3293fb2df0d64d47dfc8bb3f e6795f5325833989326a9ce3bf0f9f04861e1cf0a58d29b7a1e5fde5faf0851d 15824034529cf28c17daba1735159625e1ba14435b42c17781dc50fb2a727d6a ef6b0b25820fe11906318ac0864c99e7346c6fd7a504571b8747b501da334c88 715d5b9e69b42ea0c0ea828b653767d0032db32bc59fd98d4403fa405b 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR10 %!PS-AdobeFont-1.1: CMR10 1.00B %%CreationDate: 1992 Feb 19 19:54:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 7 /Upsilon put dup 11 /ff put dup 12 /fi put dup 13 /fl put dup 14 /ffi put dup 19 /acute put dup 33 /exclam put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 43 /plus put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 47 /slash put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 58 /colon put dup 59 /semicolon put dup 61 /equal put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 81 /Q put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 87 /W put dup 89 /Y put dup 91 /bracketleft put dup 93 /bracketright put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put readonly def /FontBBox{-251 -250 1009 969}readonly def /UniqueXX 5000793 def currentdict end currentfile eexec 8053514d28ec28da1630165fab262882d3fca78881823c5537fe6c3dda8ee5b8 97e17cb027f5c73fdbb56b0a7c25fc3512b55fe8f3acfbffcc7f4a382d8299cc 8fd37d3cea49dabdca92847af0560b404ef71134b0f3d99934fc9d0b4e602011 b9cfb856c23f958f3c5a2fbe0ef8587d1f5774879c324e51fcb22888b74f2415 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b8ba7852d84306ef094cd6c69a298aa498bacb3c71930a5ec234acc1e09fe55d 4143b9ceda49fa1d5b6ba3b4f4f3 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI10 %!PS-AdobeFont-1.1: CMMI10 1.100 %%CreationDate: 1996 Jul 23 07:53:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /alpha put dup 12 /beta put dup 13 /gamma put dup 18 /theta put dup 22 /mu put dup 23 /nu put dup 25 /pi put dup 28 /tau put dup 33 /omega put dup 34 /epsilon put dup 36 /pi1 put dup 58 /period put dup 59 /comma put dup 60 /less put dup 61 /slash put dup 62 /greater put dup 64 /partialdiff put dup 65 /A put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 72 /H put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 81 /Q put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 87 /W put dup 97 /a put dup 98 /b put dup 100 /d put dup 101 /e put dup 102 /f put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 120 /x put dup 121 /y put readonly def /FontBBox{-32 -250 1048 750}readonly def /UniqueXX 5087385 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d725e830d1c76fba12e12486e989c98 74c2b527f0925722787027f44470d484262c360cdfdddf3657533a57bb16f730 48bfbbfcb73a650484015441fdc837add94ac8fbd2022e3ec8f115d4b4bb7b7f 15388f22cc6198efe768bd9fceb3446ee4a8dc27d6cd152485384ef5f59381ff da43f2d20c8fb08aa27ab2015b774db10dacfdcd33e60f178c461553146ab427 bdd7da12534ba078ad3d780414930da4f8d58abefd45db119b10eb409dd89792 3c6e705479464a4b310b58348c4b42393988fef4925cf984423aaf65fea9f0e6 4629953bcf50b919d968d99bd185f83112b2759cc411764e9bde677f57c5ee5a c555448d5f81a16259ded1e11bf4119d53e8ab07a802df900d3a2d5ccc1c6876 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0052300cbe17668a2e8360553ac24884fcb5e240248c7c485bb424b69dac3fe5 bef3fb95c7dc578b3a0d61b5dd029b618c6fdf3aa6360c212902226397592402 629c8f293e39622e77a419e10eb025e99c973242ea08c96fdf153529269fb090 c93c9b07847d6aaae0fed0fb5802267996900fd875847d6ddddcf4f0c9601ae1 47e67bfdcfc9c16fc26897a96c6a36996240c2df4291b197fa428f993a581f35 08d6bad770d0f351ca2781c81a0c672c73087a131020864c70fd000e7b03b4c0 0d5da1e26210642f991fca7842b39c42f31c172452afe4300d3b03f9527b1634 8da371655cbc01d2640aa6c7d1e1517a61956470aa6721b68c4b083d0a25d98a 6a6e28257d533a77434b39e7618cb67d2727b2ae7a5224535d6c5a1788998670 ba634f291aa04ac2f31d7136fa448dc5ec62dd882c3911fa2af4f5d0ddd7324f 149b7221ba3901402b7a497b76e41f41a8221a9027c52ba70edb586b00e10503 7a9edbc201815d1b3c2a9c4ba331db2184ff8a38fe8750e38520a08e8a86038c b129d5575ebf00351bca6901a8ab2b836e63b59159deeae829960a47bf9c2ef0 0f1b259051f7ac538163e602836de9bf7c421e9728cb56c3647d73e9b0131bf6 8a3c7937d9102a5b7f07971cc02647c84a74ab6fcf6eda571e0e4d47dc9daf0c dc9e0b1bebc02d1444a32139e0a443c022e14ce8e5dafbe6d3f39a7e6952fed0 4c8f0931e5dfc6b6e5b4e376adae3d80b4523348e2c962c696c35f36558d20d5 e77e0d48faaadeeed564f982d8381958df6018c875bed03aac6453d021c814a9 b8cd46d2725bcd243c0bbd13fb22435b807f22747dfb86628b0438084bd8ab09 b2c3957070f030c65cb5bcddeca6c1bc94be229ad4d4aae78a0505b6ff585c9a ec 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR7 %!PS-AdobeFont-1.1: CMR7 1.0 %%CreationDate: 1991 Aug 20 16:39:21 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 40 /parenleft put dup 41 /parenright put dup 43 /plus put dup 45 /hyphen put dup 46 /period put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 59 /semicolon put dup 61 /equal put dup 65 /A put dup 68 /D put dup 69 /E put dup 75 /K put dup 77 /M put dup 79 /O put dup 82 /R put dup 86 /V put dup 97 /a put dup 109 /m put dup 120 /x put readonly def /FontBBox{-27 -250 1122 750}readonly def /UniqueXX 5000790 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 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810ae470cb4e58a98cb4b1e8fa8016db7e6ab2129f4286ee082849166c3c9f56 1ff19f5dca7e6ae795ccabe91902f2a2b860b48e6e13f75e734247ac1975a913 3d2b342e9f079a4e7fbecd8b067e38376a544ee9e9d92ec06459f1a0a1cb3b16 c60d5d3533980901ceb9d8836affd489fbed10fb8507e7e4b7145b6d0cf1dad3 7a275b314b3bc134a6a5b58b6f16a5e85bf2fc14fada04fbfe0d576923db743d fecff0976be87ce9464002ce3b081d92f7656db5c3180f9f226296471d12cb6a e38f6c9fa8f22a1a19bf82249f80f4642464049979a8d83727c751bed4418c0b 6b24502b9d59b52bc8e82498ddd77e555262bc853367a4bcb05c43d4300b715c a23c0374e35169fa436b2a3e4a5b555df6915cc24f7efb366c692cd60543ab03 faf1edca9c5c4238db6c1e15e3be64557793cf5777708e98c644146fede981d2 308dd31f853c53cce2e7edd1edccd3a6ce29eedf32c714208f8d65670dfe3eb1 a0f7216265ef8f2cc056c4c4ae58e06a47d62cf540f59981407d80e1026ea9bc f3d50cfabd6194035a734a9f030a0cd71b8b1640e6f2d72b3d2ef8ddbff01bae b2af91b58efd5ce8f07f040e34a1db1be0c612950413da9d343f2483cfb1d446 11d9d5158131764788c6bcb7d02983d7e5c088a2ca922992adbd60c1cc02521f aa2ed26c990c1eb544a1c3d8fcad47edfca497a400442d790958e357e9a56060 136729c87fede6e0807fadfc253a3fe7bbc4666680867fc09ca2a9bf0a283e6f 7ff1b0039303cc0d38ca400f6a1e3ea3d13245cb4a65c502aab6 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMTI8 %!PS-AdobeFont-1.1: CMTI8 1.0 %%CreationDate: 1991 Aug 18 21:07:42 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMTI8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMTI8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 48 /zero put dup 49 /one put dup 58 /colon put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 73 /I put dup 74 /J put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 89 /Y put dup 97 /a put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 104 /h put dup 105 /i put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u 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cleartomark %%EndFont %%BeginFont: CMTI10 %!PS-AdobeFont-1.1: CMTI10 1.00B %%CreationDate: 1992 Feb 19 19:56:16 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMTI10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMTI10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /ff put dup 12 /fi put dup 13 /fl put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 54 /six put dup 55 /seven put dup 58 /colon put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 70 /F put dup 72 /H put dup 73 /I put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 80 /P put dup 84 /T put dup 87 /W put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put readonly def /FontBBox{-163 -250 1146 969}readonly def /UniqueXX 5000828 def currentdict end currentfile eexec 8053514d28ec28da1630165fab262882d3ffd20326947b1065649b533eb5e9e3 a88a87fe987918a687950b26f647d6e08bf14d983ed1d4a8ca1e2da8d985f944 2eb916f5b6ed0697ac7c33e1e36a3bf460d34ce45f1631871097cb04f18e3889 4cf4ac1538eb19481311d24fe3be7beaa4a3730e8b4831fe59d6d9ce2e46116b 629c7ba2f9ce3ecba2f43bc162a5a077ca1b2882a42afdcec3f4b75b5d63e0bc 8e5dc95257766d8ea467ad9cbaf47be60f797580cced6884b3a68f70c91f4fdf 80fd00ed9139e7f480dc3a76af72ad9b434187730bdfaefe4cbfe5c7edcaaf24 9204fd703011932e5a3c27be468b7dab69daa18dbbb6335ab8ddfdc607961c7c 02582763fa069d43563ba17704029945cf42fcb19cf78c51df0ec4d851086d43 c1ab38e865ef36865fff3a08b01cbcb070ba4893f7482dc7819ad03d337e520e 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f48756e211f0bc76429d0595ab8e1426806c3ee0cca82da7efd410e81dc48507 a718500239ac515ec95e74fa3fbbdb6917443078aac22c93293631e89efacced 690d96087895025fa312bc8d1df91e2fdeb1f18ef1254d44242c9a57e198d2d6 1658b98942abe2ca58caa2c2dcca40796a1d88211d278612b5d918d660cbd68e 8d7e1fdfce3128e2593b67042ab88bc437921e14e1a67326cf6a45f4a2ab786a cd78c03a6e81c1682ea661ea726f8d74bd6ae4acaa84108d0e0ee3aa173367ca 54 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMCSC10 %!PS-AdobeFont-1.1: CMCSC10 1.0 %%CreationDate: 1991 Aug 18 17:46:49 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMCSC10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMCSC10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 58 /colon put dup 65 /A put dup 68 /D put dup 70 /F put dup 72 /H put dup 73 /I put dup 76 /L put dup 78 /N put dup 82 /R put dup 83 /S put dup 87 /W put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 120 /x put dup 121 /y put dup 122 /z put readonly def /FontBBox{14 -250 1077 750}readonly def /UniqueXX 5000772 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacee583a5c939393e012707b47e0c1f a47d284a1edc9d01a497d772bca8c543388e6dc0d1e2c4944740470e0914f65e fb0737b0851b2ba713a9a00b36d07da6bcb52920b9b59efe587734027a3c5e65 66aad332fe6fbcced1417802822a3b81d6187875263d6bbda04bbcf6e4870fee ad60f104bb3c5a766610dd11aea64a6b107b0b04439fa2888b8cc39232bb83f7 695aba81f0260cd5248b9e649cd800bcb325468c79ffacb9cd3037a112066957 7889d67fff57549064b985d67ede2fb03272083723541051ebe936eff01a4ab3 cd845d565dfdf25d9ddd2792db17f52f894bea484480f06c832140fdd6c3af0e fef0584c6b78b5e2bbb9a752f10581fd1c48cb498a822afb18cddebba34695b9 b418010368fdfb7bf758d50f3af03360b81c776325c33c9c81130b1e1be840cf 68c71ffd091dccc0df7b507fe8953dc3836af0da08ff9ff3e9cf7288d9eb8baf ffac546a0fd987ae8e0bcf7b759f4408e13524f478de5896d816cb0ad2904271 cbec82a5ca50f0598502b434ecd94531b4a65181b5b3afcb650904b15157737a 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6493eb4551789d9fbaa5239c17a702c9c37945fbc535dfbe08bf30d6424c2d40 d76f70ccef4881dba69f668445e62acbca5787a341b14133d1e4b07bef38ae4b 706bc003d738437e88004df9aca7d9f0d3e1f46d2d8e85f1bc28798e1d0e8a18 f21d37c307db7874689966106b1b926f565e1bbc92aa85b34d6c4d8405188637 7cbb58f927f6bd0181313a8b346c093cc3fad70fbad3d8730fb2db6a048d0298 9379f899036982e80c01b29281f4ab09b5c6effbc45f3b0f6a418289bab63dd4 5e756c00004b1c0ee63d59210688b6ad7cbdb639e29e68fe706f1755556af7ce 0753e048cd39000eb944d303a003c2ac354d8b1c80aed7287a0b0ee6fa64322d 5ea239a27dc512ce1c001a492cc35060e9c2b70a83d2f9d6e927e6775cf7f905 fdfe42fb269ff7662535ea9e0b4a3c85da771759a2ae8ef927d48ba55925e649 ac50564c9085baa758290fecfe4593d14ef3ee70034d102fca0df2782e24c298 c2551d8b00fb8286a52f3742e5b4b9b88792fad6d6d9b24ffd72615b29963889 063485c46f17c7ae9418eb28aff56583c858c963bec961ad88727eb94e676d21 98777ea00150b48ec3d25f41df48921ad4517a98a38ade 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR6 %!PS-AdobeFont-1.1: CMR6 1.0 %%CreationDate: 1991 Aug 20 16:39:02 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 48 /zero put dup 49 /one put dup 50 /two put readonly def /FontBBox{-20 -250 1193 750}readonly def /UniqueXX 5000789 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3 2ba0357b5e050fddf264a07470bef1c52119b6fbd5c77ebed964ac5a2bbec9d8 b3e48ae5bb003a63d545774b922b9d5ff6b0066ece43645a131879b032137d6d 823385fe55f3402d557fd3b4486858b2a4b5a0cc2e1bf4e2a4a0e748483c3bcf 5de47cc5260a3a967cac70a7a35b88b54315191d0423b4065c7a432987938c6b edad3b72ad63c2918b6e5a2017457e0d4ebc204b031f3fc6c13d7da7277a94ba 018e9998b3dd888011a5d7c4204989f30f908b95533bda845746b673ab71ea57 65a0d14f4350707e47c8276305b28513cbe1bb0dbd269a53719bda46e536685d df78ca0146b6b93e760256b74d939d4e35b5e77238f04c92298dfdd188feea30 e053eefbcbb52f2011772b3aae39f5805597bbc1e8bb75a446ce014030f4f2f0 f49f9e962ee4a1024a746fa92a3628db5270732b54e43fe5ecfa524f127e5fcc 788e77e66098336ad67fe4cccaf0253272d5df79864bf4b734cb9a5859d557d8 bc11b8e00221ebc12e97de4b1f466ead83a4c894709363bca9040410a52d592e 34ee40cc7e5efa920546b981aa659513a24b1b85c221a1875b62d0b89e57a368 321b8043a5b094e0379760a443d632892b14ad6d19dacc8c78093243ad67e6a3 08e56e6b68412ee690b10dac6e17708754a00d51fc957b500eb80175716eef4b 2ca1ef867614659bee3f2b7319e97b6fdf1efc847bf3cee3156f72f21751da8e 5fb6898919e6799820d3de0642d756e09d6fae4ff08dd3deda3173bff4bb11f7 9109c97ddc05897af709ea199a90fcee8ce4c7a3c15b18170c41c04de2d3fba8 f34296a95b8e1e8de3739b17273f8f2c85e914615e8eac5e8bd2387ba3b1edf4 7968f06e2067d836d0f9f3e085cdfd2de06a62c81d786b304326f7002e83160a 36598589228b4dddddc43c85e1d126f8fe81b828028e26317af5894aaccf4f69 6301e1a9fc45935d8a414957f08febebbc3a72ada80f101e47447d019ade56e9 f4fab969bba2b44e47399fedf5caa1bcea216d7ba713d523d98f2e44ef37ad46 282d7a587974734c2b1e24d854562df98bbe4af15005486cbaffcbcffec311bd e91d2cadb4d2d0835a77c4f73bdee2dd107a4700b60cf0bff46d3d25dfaf0551 8e363c1e95736e70a5c950a2152ce2c3f5c44389518fcb2cc85003fc99994abd 691177ab02601cc9e72a98c68c487b6251ee3b4b649aa85afa307fa744c5baa1 6bd6170fa6404f15b42eb9d417e3fb0f48335c6db453bb0a46a730ab26c3f903 9db1f048f083a04fd61a35caef7d527d21ae534ea61c9798e5c1c802796207f4 89c987f0d56276e362a5347f3b005aab26da5ab14d146d495dd58daedc16fee1 bbd150e48676b71b6cc41348b2526346ff01806a0143c9ed4deb60706f4e34ce 46615c7501249491edb50dc52846399ce5e2a406f7449488d54f6bfa9e1c2bb6 17a90981965b9de4db15b0afe8f45b3882eab15a0c8e5f79c3b2ee8518b0fe62 3bf01f7307d234cadb7d2a0fa3106a51e358ff843df209a9ac21b085d85486d1 294c4703dbba4d7e87d6d534c8c57640530f21a659f6627ee65d9d8a6259e1f3 c4e49b7b475f2cf3811da2863c314146d835b045fe89196581d4a25eb2451356 e234d3e173047a7dae601dfb357131be9b8099688c3039507b46e692e58fd35e 72ee7c8093254fb3138bebc6b5370cba404919b7760eb0c4b0524b2f56ba7673 3a5c7bcba15bbc1d5ba98e5f426e91586683bcdf974b824c76cd302d0843e130 52c69d22034b0a5c9fbf20702c06370b2073de16ae3a459371f9591be5cf651f 1a24912c63330430ef6e 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY8 %!PS-AdobeFont-1.1: CMSY8 1.0 %%CreationDate: 1991 Aug 15 07:22:10 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 49 /infinity put dup 93 /unionmulti put readonly def /FontBBox{-30 -955 1185 779}readonly def /UniqueXX 5000818 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bac8ced9b09a275ab231194ecf829352 05826f4e975dcecec72b2cf3a18899ccde1fd935d09d813b096cc6b83cdf4f23 b9a60db41f9976ac333263c908dcefcdbd4c8402ed00a36e7487634d089fd45a f4a38a56a4412c3b0baffaeb717bf0de9ffb7a8460bf475a6718b0c73c571145 d026957276530530a2fbefc6c8f059084178f5ab59e11b66566ca5ba42b1911a 5d7f1bf343015eece988b7a93bce0c7aa61344d48aed9c92c8698d4b7c9951c8 7d103f2414b39e1437f9d2e50c4ee5f218f2e6716926a79ea978f13b1f855345 191dd7d31d8f82c2e3343c7a5894d95bdc492c28226834efcb5c12fea36ac5cc 430e0aa604961e34888adf6c1f3954cbc2498e225d953cf5685852162346f474 5a2a7087d5d7ad486de16d2ca8e15cee26e012671ba3bdc7d95cc8c98bb774f5 08625e968aee27ff7d1a06e63bcfb5aa4876c3f8f13b30ccccee73c3caf4e70d 98e6ed2f422dbb4950bf789680e064150995941a9f4dd68a575949847a7d012b b910bf03a69374e341e8036ff92c949f3dc6e86aaa7a2b795ba5139b2479d20e 3ea5df0663c26a3fa694b559e58cef0724c4641b9190df3e50671822dbae06a6 ebd26110a7f7776577e94c046c3838d691d0a81539f92f25be7ef477fbaffce0 301c1aeba1a7b416c57ab22f4588d470823ab484ed6257d0a93cf0b8600968bf cfc6c7abf89ff09f478943c962bca0b1b99c4973f8c65dd9addcc0236d2d7a02 ad8b50560a44fb33e3560324b17aa351d14372d0a6e561070a23172b57d60997 d259f2f61de4dfc6e13bf856df493c1b0190dd25e37cf3159e2f860a608721f9 8b85d6ba147bffbe7180c1b1d675416caea3d5235c909bf6e8bf78f89f50d00c b33807c366e4389611f2ec90f1954cad000392c01c02fef9353338ed14fcdf17 fa3c876573c59986201af5c671cb745ff7d3e12dac2405f02a34fe2be96460cf 2a37b6e85eb7512b60b5d3ee3963142eb301bddcb3e6e75c3cd688f969633ab4 926bcbfbfc897425709d0c4e2a3630d80d6ca34b9ce8f15ba9bb239fc358caa0 aac96976344208d6bb3eca4eeca666b6a57dc26ef6196c305273d8725a7002aa 2666386ffe38c4e7529a216f702cf08519185670f5359c719c20364945c80259 67326e720e01ab33afb491307674fae163b29e51aaa0e1d8e8c4b764daf0b0d9 64b1882b66118eb8d45f56bc8124a7bfd059c2ea576775c383d4df64b0c7112f cf36eec68f15aef3238035a2bde6c5faf51e 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI8 %!PS-AdobeFont-1.1: CMMI8 1.100 %%CreationDate: 1996 Jul 23 07:53:54 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 22 /mu put dup 23 /nu put dup 33 /omega put dup 58 /period put dup 59 /comma put dup 67 /C put dup 68 /D put dup 69 /E put dup 82 /R put dup 105 /i put dup 112 /p put readonly def /FontBBox{-24 -250 1110 750}readonly def /UniqueXX 5087383 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d725e830d1c76fba12e12486e989c98 74c2b527f0925722787027f44470d484262c360cdfdddf3657533a57bb16f730 48bfbbfcb73a650484015441fdc837add94ac8fbd2022e3ec8f115d4b4bb7b7f 15388f22cc6198efe768bd9fceb3446ee4a8dc27d6cd152485384ef5f59381ff da43f2d20c8fb08aa27ab2015b774db10dacfdcd33e60f178c461553146ab427 bdd7da12534ba078ad3d780414930e72218b3075925ce1192f11fc8530fcd5e3 038e3a6a6db2dcfbae3b4653e7e02730314e02b54a1e296d2bef8a79411d9225 dad7b4e6d6f9cf0688b69ba21193bf1495807e7a196cf14c95a4e02f9cd2da8c db2546c6df52e524745992e18d9ff87aa25e4e1800bbe4ebb357c6ef55ed6d03 6d3a00c1ee8073266c21d2f0ac85d656abf61d7e5a4fa87da8ec3b5329e434d0 d2adab706b42a2e5331be5295399d803ccac03f631f01f39a022fcdf63486b68 7d15ef284a77def7fde4898543e7b5f7ec267756103e477f547cfb8d2311c4b0 09deff56085f5d419697af1846c8b88c1bbbae149f0f19ca3c8dafe19cec48fe 6b38357246d8b5cef80b53bab4cbbbe8bc8318cc462a4158258f456e697f6058 86010493f252073ee4e4c9531f23485415ad6bc901bbaea659ef701f825f4b6d 5c9bed0dce7b63810f906b33ea4955531ca1ed1fc120cc56dc1e277a33222cc6 c3a97552607b865783faf0895cbeccd0df54f57bd162a88494768435eda71a39 69718c0c5912d3167bb0971546d733e735aa9bcd89f5aa154656031ab3f6fe41 94ec225ad03ab8b67a9da43ab365c4df17c23e79f685c3b6fd5b654e4a6f2603 6cec3a8641b0b57f93eb95f9e238832aeac2061f3153e0f375513c974f1c38f7 b59edcc94716f2862cf71c9a2be8430985da1cd813b1e1c1b9310564a2e9bdb8 c536db7caeb9c37a0693a01df0045080f8236ece54dcfa7b743562771f452398 100dd95b678b6f190cdef25df0e2b10423aef1d27dfd5b022a0f895423aebb50 34ea52f46b077f2022e28ecfa6137fdd4b13935ac19769600b2e0dc86b0a2359 4675106e26eea6b5033525c1d79e046ee941c9ad410ad3284092f9fb725d366e e88a7a4ceaa6caf2ff6a2c80749780481db49bf09d5b7dd77cb83ed6c74fe223 0076eb41e5e84c5f714b9cd7ae6b36396bb68c992ac812a85b87db809bcac7b8 aebf6e3d7187e77200d6e69933253a0d7cf9263f474b9c16e87777c8b8de20ec 92259056fd54a4df1b4129338d5c2ed9aeb35ca5315ac364f1a5810c7741d796 ea6027b269d7596a95c04f66eeed7c3bda282773bb4b078d280999b1ba6b266f 7bf18aed1487ca4d9e2eb94f57d79bf5f939fc60d5293c72ec8372f6bc410806 459b05e9ae03dfa4b3cbe2b80dee6c83fda864f0e4e1ba22ed2d33b439c8a72b d9bf50744a8134faab0a1798f82116b67fd242b300d5f84244da57f0dc7fc63a 9b2c1beebc305052ff60b567fb57717f2282d052ca0246b42899883598b9187b 0aa927a5ed1cb11e77aa1e2e6250e721822b49beacdc00cf97a52f2de46451bb 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5a24a39b8fcc3f622a0e7b0ee6f2e547055ad6c340ce55e6fe605bdeba40c14e 60d99d3b0d6e40b6a05ee9d66fff800dec6dbf 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR8 %!PS-AdobeFont-1.1: CMR8 1.0 %%CreationDate: 1991 Aug 20 16:39:40 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /ff put dup 12 /fi put dup 13 /fl put dup 16 /dotlessi put dup 19 /acute put dup 20 /caron put dup 21 /breve put dup 40 /parenleft put dup 41 /parenright put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 58 /colon put dup 61 /equal put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 74 /J put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 87 /W put dup 89 /Y put dup 91 /bracketleft put dup 93 /bracketright put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put dup 123 /endash put dup 126 /tilde put readonly def /FontBBox{-36 -250 1070 750}readonly def /UniqueXX 5000791 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3 2ba0357b5e050fddf264a07470bef1c52119b6fbd5c77ebed964ac5a2bbec9d8 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45 v 17138 69541 a(d)p 17714 68727 400 45 v(t)18646 68760 y Fs(=)p 19814 68151 577 45 v 307 w Fn(v)20390 68926 y Fo(0)20887 68760 y Fs(\()p 21317 68151 633 45 v Fn(x;)p 22441 68151 583 45 v 184 w(y)41 b Fs(;)184 b Fn(\027)70 b Fs(\))247 b(+)f Fn(A)p 26747 68151 577 45 v(v)27324 68926 y Fo(1)27820 68760 y Fs(\()p 28250 68151 633 45 v Fn(x)q(;)p 29375 68151 583 45 v 184 w(y)40 b(;)p 30449 68151 729 45 v 184 w(!)p 31179 67947 400 45 v 41 w(t)245 b Fs(+)h Fn(\022)31 b Fs(;)184 b Fn(\027)70 b Fs(\))p eop %%Page: 5 5 5 4 bop 10902 3345 a Fm(FREQUENCY)389 b(SP)-101 b(ANNING)388 b(HOMOCLINIC)f(F)-135 b(AMILIES.)4774 b Fo(5)9924 6001 y Fs(with)371 b(the)e(t)-31 b(w)g(o)371 b(non-dimensional)h(parameters) e Fn(A;)p 31743 5392 729 45 v 184 w(!)410 b Fs(:)16105 8572 y Fn(A)p Fs(\()p Fn(\027)70 b Fs(\))309 b(=)20022 7823 y Fn(W)21067 7989 y Fo(1)21564 7823 y Fs(\()p Fn(\027)70 b Fs(\))p 20022 8318 3021 45 v 20022 9331 a Fn(W)21067 9497 y Fo(0)21564 9331 y Fs(\()p Fn(\027)g Fs(\))23175 8572 y Fn(;)p 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b(y)360 b(that)i Fn(p)32061 18941 y Ff(r)32472 19052 y Fh(n)33015 18941 y Fo(\()p Ff(\027)52 b Fo(\))34618 19343 y Fs(undergo)31 b(es)360 b(a)h(homo)31 b(clinic)6075 20671 y(bifurcation)250 b(at)f Fn(\027)13363 20837 y Ff(i)13980 20671 y Fs(if)g Fn(p)15431 20269 y Ff(r)15842 20380 y Fh(n)16384 20269 y Fo(\()p Ff(\027)17174 20380 y Fi(1)17606 20269 y Fo(\))18256 20671 y Fs(is)f(a)h(tangen)-31 b(t)250 b(homo)31 b(clinic)251 b(orbit.)453 b(Next)249 b(w)-31 b(e)249 b(construct)f(a)h(lab)31 b(eling)6075 21999 y(of)369 b(the)h(orbits)f(in)h Fn(P)154 b Fs(\()p Fn(\027)70 b Fs(\))370 b(whic)-31 b(h)370 b(is)f(con)-31 b(v)g(enien)g(t)371 b(ev)-31 b(en)370 b(across)e(homo)31 b(clinic)372 b(bifurcations.)6075 24024 y Fg(Lemma)382 b(1.)522 b Fq(Consider)363 b(a)g(fr)-57 b(e)g(quency)366 b(sp)-57 b(anning)364 b(homo)-57 b(clinic)365 b(family.)500 b(Then,)370 b(ther)-57 b(e)363 b(exists)g(a)6075 25352 y(lab)-57 b(eling)303 b(scheme)f(for)g(the)f(primary)i(homo)-57 b(clinic)303 b(orbits)e(satisfying)j(the)d(fol)57 b(lowing)302 b(pr)-57 b(op)g(erties:)7957 26941 y Fs(\(1\))554 b Fn(r)31 b Fs(\()p Fn(\027)70 b Fs(\))459 b Fq(is)f(pie)-57 b(c)g(ewise)459 b(c)-57 b(onstant,)473 b(changing)458 b(only)g(at)f(values)g(of)h Fn(\027)528 b Fq(at)457 b(which)g Fn(p)42770 26539 y Ff(r)24 b Fo(\()p Ff(\027)52 b Fo(\))44447 26941 y Fs(\()p Fn(\027)70 b Fs(\))9924 28269 y Fq(under)-57 b(go)g(es)397 b(a)f(homo)-57 b(clinic)398 b(bifur)-57 b(c)g(ation.)7957 29598 y Fs(\(2\))554 b Fq(The)432 b(lab)-57 b(eling)433 b(scheme)e(r)-57 b(esp)g(e)g(cts)432 b(the)f(unstable)h(or)-57 b(dering,)441 b(so)431 b(that)f Fn(r)39421 29764 y Ff(n)40024 29598 y Fs(\()p Fn(\027)70 b Fs(\))373 b Fn(<)f(r)43606 29764 y Ff(m)44447 29598 y Fs(\()p Fn(\027)70 b Fs(\))9924 31141 y Fq(i\013)397 b Fn(p)11896 30566 y Ff(r)12307 30677 y Fh(n)12850 30566 y Fo(\()p Ff(\027)52 b Fo(\))11896 31437 y(0)14092 31141 y Fs(\()p Fn(\027)70 b Fs(\))309 b Fn(<)16739 31307 y Ff(u)17625 31141 y Fn(p)18182 30566 y Ff(r)18593 30677 y Fh(m)19328 30566 y Fo(\()p Ff(\027)52 b Fo(\))18182 31437 y(0)20571 31141 y Fs(\()p Fn(\027)70 b Fs(\))p Fq(,)398 b(namely)f(\(se)-57 b(e)396 b Fs([3)q(])p Fq(\):)6075 32991 y Fs(\(3.2\))5690 b Fn(U)121 b Fs([)p Fn(\015)61 b Fs(\()p Fn(\027)70 b Fs(\))p Fn(;)184 b(p)18381 32499 y Ff(r)18792 32610 y Fh(n)18381 33286 y Fo(0)19393 32991 y Fs(\()p Fn(\027)70 b Fs(\)])309 b Fl(\032)f Fn(U)121 b Fs([)p Fn(\015)61 b Fs(\()p Fn(\027)70 b Fs(\))p Fn(;)184 b(p)26998 32499 y Ff(r)27409 32610 y Fh(m)26998 33286 y Fo(0)28202 32991 y Fs(\()p Fn(\027)70 b Fs(\)])1190 b Fq(for)e Fn(r)34235 33157 y Ff(n)35146 32991 y Fn(<)307 b(r)36813 33157 y Ff(m)37654 32991 y Fn(:)6075 35015 y Fq(Pr)-57 b(o)g(of.)554 b Fs(By)452 b(construction.)740 b(W)-92 b(e)450 b(construct)i(suc)-31 b(h)451 b(a)g(lab)31 b(eling)454 b(sc)-31 b(heme)451 b(inductiv)-31 b(ely)-92 b(,)474 b(in)452 b(the)6075 36344 y(in)-31 b(terv)-61 b(als)370 b(\()p Fn(\027)11489 36510 y Ff(k)12034 36344 y Fn(;)184 b(\027)13072 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y(0)40703 56165 y Fs(\()p Fn(\027)70 b Fs(\),)351 b(satisfy)6075 57493 y Fl(j)p Fn(@)61 b(R)7881 57092 y Fo(1)7872 57768 y(0)8377 57493 y Fs(\()p Fn(\027)70 b Fs(\))p Fl(j)309 b Fs(=)f(min)13484 57659 y Ff(i)14037 57493 y Fl(j)p Fn(@)61 b(R)15843 57092 y Fo(1)15834 57782 y Ff(i)16339 57493 y Fs(\()p Fn(\027)70 b Fs(\))p Fl(j)p Fs(.)458 b(When)261 b(there)h(are)f(no)h(degeneracies)f(\(here,)284 b(when)261 b(the)h(maximal)6075 58822 y(area)370 b(is)g(ac)-31 b(hiev)g(ed)371 b(at)f(a)h(unique)f(orbit)h(and)f(the)g(minimal)i(b)31 b(oundary)370 b(length)h(is)f(ac)-31 b(hiev)g(ed)371 b(at)6075 60150 y(a)387 b(unique)g(homo)31 b(clinic)389 b(p)31 b(oin)-31 b(t\))389 b(this)e(pro)31 b(cedure)386 b(determines)h(uniquely)h(the)f(lab)31 b(eling)389 b(of)e(the)6075 61478 y(top)31 b(ologically)422 b(transv)-31 b(erse)417 b(homo)31 b(clinic)420 b(orbits)e(for)f(0)388 b Fn(<)g(\027)459 b(<)387 b(\027)33477 61644 y Fo(1)33974 61478 y Fn(:)418 b Fs(If)f(a)h(degeneracy)f(o)31 b(ccurs,)6075 62807 y(c)-31 b(ho)31 b(ose)446 b(an)-31 b(y)446 b(one)g(of)h(the)f(\014nite)g(n)-31 b(um)g(b)31 b(er)446 b(of)g(the)g(maximizing)j(\(resp)31 b(ectiv)-31 b(ely)447 b(minimizing\))6075 64135 y(orbits)369 b(\(resp)31 b(ectiv)-31 b(ely)371 b(p)31 b(oin)-31 b(ts\).)7403 65476 y(Giv)g(en)345 b(the)g(lab)31 b(eling)347 b Fn(Lbl)22 b Fs(\()p Fn(\027)19220 65002 y Fo(+)19150 65810 y Ff(k)d Fk(\000)p Fo(1)20828 65476 y Fs(\))308 b(=)g Fl(f)p Fn(r)23787 65642 y Fo(1)24284 65476 y Fn(;)184 b(r)25274 65642 y Fo(2)25772 65476 y Fn(;)g(:::;)g(r)28174 65676 y Ff(N)83 b Fo(\()p Ff(\027)52 b Fo(\))30205 65476 y Fl(g)p Fs(,)350 b(for)345 b Fn(k)e Fl(\025)307 b Fs(1,)350 b(so)345 b(that)h Fn(Lbl)22 b Fs(\()p Fn(\027)42718 65002 y Fo(+)42648 65810 y Ff(k)d Fk(\000)p Fo(1)44326 65476 y Fs(\))308 b(=)6075 66966 y Fn(Lbl)22 b Fs(\()p Fn(\027)70 b Fs(\))370 b(for)g Fn(\027)377 b Fl(2)308 b Fs(\()p Fn(\027)14144 67132 y Ff(k)19 b Fk(\000)p Fo(1)15822 66966 y Fn(;)184 b(\027)16860 67132 y Ff(k)17405 66966 y Fs(\),)370 b(w)-31 b(e)370 b(construct)g Fn(Lbl)22 b Fs(\()p Fn(\027)27637 66492 y Fo(+)27567 67300 y Ff(k)28373 66966 y Fs(\))369 b(as)g(follo)-31 b(ws:)p 6075 68221 6642 45 v 7403 69198 a Fo(2)7844 69541 y Fx(By)314 b(area)g(preserv)-52 b(ation)314 b Fv(\026)p Fx(\()p Fv(R)18319 69125 y Fe(r)18704 69236 y Fh(n)18314 69835 y Fe(i)19302 69541 y Fx(\()p Fv(\027)58 b Fx(\)\))261 b(=)g Fv(\026)p Fx(\()p Fv(R)23821 69125 y Fe(r)24206 69236 y Fh(n)23816 69823 y Ft(0)24804 69541 y Fx(\()p Fv(\027)58 b Fx(\)\))313 b(for)g(all)i Fv(i:)p eop %%Page: 7 7 7 6 bop 10902 3345 a Fm(FREQUENCY)389 b(SP)-101 b(ANNING)388 b(HOMOCLINIC)f(F)-135 b(AMILIES.)4774 b Fo(7)8677 18513 y @beginspecial 0 @llx 0 @lly 575 @urx 215 @ury 3118 @rwi @setspecial %%BeginDocument: fig2.eps %!PS-Adobe-3.0 EPSF-3.0 %%Creator: (ImageMagick) %%Title: (fig2.eps) %%CreationDate: (Thu Dec 19 11:21:21 2002) %%BoundingBox: 0 0 575 215 %%DocumentData: Clean7Bit %%LanguageLevel: 1 %%Pages: 0 %%EndComments %%BeginDefaults %%PageOrientation: 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The image is displayed in color on % Postscript viewers or printers that support color, otherwise % it is displayed as grayscale. % /buffer 512 string def /byte 1 string def /color_packet 3 string def /pixels 768 string def /DirectClassPacket { % % Get a DirectClass packet. % % Parameters: % red. % green. % blue. % length: number of pixels minus one of this color (optional). % currentfile color_packet readhexstring pop pop compression 0 gt { /number_pixels 3 def } { currentfile byte readhexstring pop 0 get /number_pixels exch 1 add 3 mul def } ifelse 0 3 number_pixels 1 sub { pixels exch color_packet putinterval } for pixels 0 number_pixels getinterval } bind def /DirectClassImage { % % Display a DirectClass image. % systemdict /colorimage known { columns rows 8 [ columns 0 0 rows neg 0 rows ] { DirectClassPacket } false 3 colorimage } { % % No colorimage operator; convert to grayscale. % columns rows 8 [ columns 0 0 rows neg 0 rows ] { GrayDirectClassPacket } image } ifelse } bind def /GrayDirectClassPacket { % % Get a DirectClass packet; convert to grayscale. % % Parameters: % red % green % blue % length: number of pixels minus one of this color (optional). % currentfile color_packet readhexstring pop pop color_packet 0 get 0.299 mul color_packet 1 get 0.587 mul add color_packet 2 get 0.114 mul add cvi /gray_packet exch def compression 0 gt { /number_pixels 1 def } { currentfile byte readhexstring pop 0 get /number_pixels exch 1 add def } ifelse 0 1 number_pixels 1 sub { pixels exch gray_packet put } for pixels 0 number_pixels getinterval } bind def /GrayPseudoClassPacket { % % Get a PseudoClass packet; convert to grayscale. % % Parameters: % index: index into the colormap. % length: number of pixels minus one of this color (optional). % currentfile byte readhexstring pop 0 get /offset exch 3 mul def /color_packet colormap offset 3 getinterval def color_packet 0 get 0.299 mul color_packet 1 get 0.587 mul add color_packet 2 get 0.114 mul add cvi /gray_packet exch def compression 0 gt { /number_pixels 1 def } { currentfile byte readhexstring pop 0 get /number_pixels exch 1 add def } ifelse 0 1 number_pixels 1 sub { pixels exch gray_packet put } for pixels 0 number_pixels getinterval } bind def /PseudoClassPacket { % % Get a PseudoClass packet. % % Parameters: % index: index into the colormap. % length: number of pixels minus one of this color (optional). % currentfile byte readhexstring pop 0 get /offset exch 3 mul def /color_packet colormap offset 3 getinterval def compression 0 gt { /number_pixels 3 def } { currentfile byte readhexstring pop 0 get /number_pixels exch 1 add 3 mul def } ifelse 0 3 number_pixels 1 sub { pixels exch color_packet putinterval } for pixels 0 number_pixels getinterval } bind def /PseudoClassImage { % % Display a PseudoClass image. % % Parameters: % class: 0-PseudoClass or 1-Grayscale. % currentfile buffer readline pop token pop /class exch def pop class 0 gt { currentfile buffer readline pop token pop /depth exch def 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Fn(\027)70 b Fs(\))p Fl(g)p Fn(:)6075 62363 y Fs(By)493 b(construction,)525 b(for)493 b(0)513 b Fn(<)h(\027)583 b(<)513 b(\027)22051 62529 y Fo(1)22548 62363 y Fs(,)524 b Fn(r)23878 62529 y Ff(k)24936 62363 y Fs(=)513 b Fn(k)35 b(;)493 b Fs(or)g(equiv)-61 b(alen)-31 b(tly)-92 b(,)526 b Fn(k)35 b Fs(\()p Fn(r)c Fs(;)184 b Fn(\027)70 b Fs(\))516 b(=)d Fn(r)31 b Fs(.)863 b(On)493 b(the)6075 63692 y(other)356 b(hand,)k(for)c Fn(\027)14248 63858 y Fo(1)15052 63692 y Fn(<)307 b(\027)378 b(<)308 b(\027)18861 63858 y Fo(2)19357 63692 y Fs(,)359 b(for)d(the)h(generic) f(case)g(of)h(\(3.4\))i(w)-31 b(e)356 b(ha)-31 b(v)g(e)357 b Fn(Lbl)22 b Fs(\()p Fn(\027)70 b Fs(\))p Fl(j)41068 63858 y Ff(\027)41512 63969 y Fi(1)41947 63858 y Ff(<\027)52 b(<\027)44271 63969 y Fi(2)45064 63692 y Fs(=)6075 65020 y Fl(f)p Fs(1)p Fn(;)184 b Fs(2)p Fn(;)g(::;)g(j)r(;)g(j)r(:)p Fs(1)p Fn(;)g(j)r(:)p Fs(2)p Fn(;)g(j)318 b Fs(+)246 b(1)p Fn(;)184 b(:::;)g(N)121 b Fs(\(0)20718 64618 y Fo(+)21458 65020 y Fs(\))p Fl(g)309 b Fs(=)e Fl(f)p Fn(r)24970 65186 y Fo(1)25468 65020 y Fn(;)184 b(::;)g(r)27563 65229 y Ff(N)83 b Fo(\(0)29134 65008 y Fi(+)29762 65229 y Fo(\)+2)31284 65020 y Fl(g)369 b Fs(so)8652 68268 y Fn(k)35 b Fs(\()p Fn(r)c Fs(;)184 b Fn(\027)70 b Fs(\))310 b(=)13239 65999 y Fj(8)13239 66995 y(<)13239 68987 y(:)14777 66928 y Fn(r)3721 b Fs(for)369 b Fn(r)338 b Fl(\024)308 b Fn(j)14777 68257 y Fs([)p Fn(r)31 b Fs(])247 b(+)f([\()p Fn(r)278 b Fl(\000)246 b Fs([)p Fn(r)31 b Fs(]\))247 b Fl(\001)g Fs(10])1108 b(for)369 b Fn(j)i(<)308 b(r)338 b(<)308 b(j)h Fs(+)246 b(1)14777 69585 y Fn(r)277 b Fs(+)246 b(2)1107 b(for)369 b Fn(r)339 b Fl(\025)307 b Fn(j)j Fs(+)246 b(1)p Fn(;)35629 68268 y Fs(for)738 b Fn(\027)38239 68434 y Fo(1)39043 68268 y Fn(<)308 b(\027)377 b(<)308 b(\027)42852 68434 y Fo(2)p eop %%Page: 8 8 8 7 bop 6075 3345 a Fo(8)14831 b(VERED)299 b(R)-24 b(OM-KED)g(AR.)8677 18081 y @beginspecial 0 @llx 0 @lly 575 @urx 215 @ury 3118 @rwi @setspecial %%BeginDocument: fig3.eps %!PS-Adobe-3.0 EPSF-3.0 %%Creator: (ImageMagick) %%Title: (fig3.eps) %%CreationDate: (Thu Dec 19 11:21:36 2002) %%BoundingBox: 0 0 575 215 %%DocumentData: Clean7Bit %%LanguageLevel: 1 %%Pages: 0 %%EndComments %%BeginDefaults %%PageOrientation: Portrait %%EndDefaults %%BeginProlog % % Display a color image. The image is displayed in color on % Postscript viewers or printers that support color, otherwise % it is displayed as grayscale. % /buffer 512 string def /byte 1 string def /color_packet 3 string def /pixels 768 string def /DirectClassPacket { % % Get a DirectClass packet. % % Parameters: % red. % green. % blue. % length: number of pixels minus one of this color (optional). % currentfile color_packet readhexstring pop pop compression 0 gt { /number_pixels 3 def } { currentfile byte readhexstring pop 0 get /number_pixels exch 1 add 3 mul def } ifelse 0 3 number_pixels 1 sub { pixels exch color_packet putinterval } for pixels 0 number_pixels getinterval } bind def /DirectClassImage { % % Display a DirectClass image. % systemdict /colorimage known { columns rows 8 [ columns 0 0 rows neg 0 rows ] { DirectClassPacket } false 3 colorimage } { % % No colorimage operator; convert to grayscale. % columns rows 8 [ columns 0 0 rows neg 0 rows ] { GrayDirectClassPacket } image } ifelse } bind def /GrayDirectClassPacket { % % Get a DirectClass packet; convert to grayscale. % % Parameters: % red % green % blue % length: number of pixels minus one of this color (optional). % currentfile color_packet readhexstring pop pop color_packet 0 get 0.299 mul color_packet 1 get 0.587 mul add color_packet 2 get 0.114 mul add cvi /gray_packet exch def compression 0 gt { /number_pixels 1 def } { currentfile byte readhexstring pop 0 get /number_pixels exch 1 add def } ifelse 0 1 number_pixels 1 sub { pixels exch gray_packet put } for pixels 0 number_pixels getinterval } bind def /GrayPseudoClassPacket { % % Get a PseudoClass packet; convert to grayscale. % % Parameters: % index: index into the colormap. % length: number of pixels minus one of this color (optional). % currentfile byte readhexstring pop 0 get /offset exch 3 mul def /color_packet colormap offset 3 getinterval def color_packet 0 get 0.299 mul color_packet 1 get 0.587 mul add color_packet 2 get 0.114 mul add cvi /gray_packet exch def compression 0 gt { /number_pixels 1 def } { currentfile byte readhexstring pop 0 get /number_pixels exch 1 add def } ifelse 0 1 number_pixels 1 sub { pixels exch gray_packet put } for pixels 0 number_pixels getinterval } bind def /PseudoClassPacket { % % Get a PseudoClass packet. % % Parameters: % index: index into the colormap. % length: number of pixels minus one of this color (optional). % currentfile byte readhexstring pop 0 get /offset exch 3 mul def /color_packet colormap offset 3 getinterval def compression 0 gt { /number_pixels 3 def } { currentfile byte readhexstring pop 0 get /number_pixels exch 1 add 3 mul def } ifelse 0 3 number_pixels 1 sub { pixels exch color_packet putinterval } for pixels 0 number_pixels getinterval } bind def /PseudoClassImage { % % Display a PseudoClass image. % % Parameters: % class: 0-PseudoClass or 1-Grayscale. % currentfile buffer readline pop token pop /class exch def pop class 0 gt { currentfile buffer readline pop token pop /depth exch def 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Fn(\027)378 b Fs(=)p Fn(\027)p 11846 22027 618 45 v 439 w Fs(where)369 b Fn(\027)16580 22016 y Fo(1)17384 21850 y Fn(<\027)p 18245 22027 V 70 w(<)307 b(\027)20577 22016 y Fo(2)21443 21850 y Fs(see)368 b(\014gure)h(5.)8677 36640 y @beginspecial 0 @llx 0 @lly 575 @urx 215 @ury 3118 @rwi @setspecial %%BeginDocument: fig4.eps %!PS-Adobe-3.0 EPSF-3.0 %%Creator: (ImageMagick) %%Title: (fig4.eps) %%CreationDate: (Thu Dec 19 11:21:43 2002) %%BoundingBox: 0 0 575 215 %%DocumentData: Clean7Bit %%LanguageLevel: 1 %%Pages: 0 %%EndComments %%BeginDefaults %%PageOrientation: Portrait %%EndDefaults %%BeginProlog % % Display a color image. The image is displayed in color on % Postscript viewers or printers that support color, otherwise % it is displayed as grayscale. % /buffer 512 string def /byte 1 string def /color_packet 3 string def /pixels 768 string def /DirectClassPacket { % % Get a DirectClass packet. % % Parameters: % red. % green. % blue. % length: number of pixels minus one of this color (optional). % currentfile color_packet readhexstring pop pop compression 0 gt { /number_pixels 3 def } { currentfile byte readhexstring pop 0 get /number_pixels exch 1 add 3 mul def } ifelse 0 3 number_pixels 1 sub { pixels exch color_packet putinterval } for pixels 0 number_pixels getinterval } bind def /DirectClassImage { % % Display a DirectClass image. % systemdict /colorimage known { columns rows 8 [ columns 0 0 rows neg 0 rows ] { DirectClassPacket } false 3 colorimage } { % % No colorimage operator; convert to grayscale. % columns rows 8 [ columns 0 0 rows neg 0 rows ] { GrayDirectClassPacket } image } ifelse } bind def /GrayDirectClassPacket { % % Get a DirectClass packet; convert to grayscale. % % Parameters: % red % green % blue % length: number of pixels minus one of this color (optional). % currentfile color_packet readhexstring pop pop color_packet 0 get 0.299 mul color_packet 1 get 0.587 mul add color_packet 2 get 0.114 mul add cvi /gray_packet exch def compression 0 gt { /number_pixels 1 def } { currentfile byte readhexstring pop 0 get /number_pixels exch 1 add def } ifelse 0 1 number_pixels 1 sub { pixels exch gray_packet put } for pixels 0 number_pixels getinterval } bind def /GrayPseudoClassPacket { % % Get a PseudoClass packet; convert to grayscale. % % Parameters: % index: index into the colormap. % length: number of pixels minus one of this color (optional). % currentfile byte readhexstring pop 0 get /offset exch 3 mul def /color_packet colormap offset 3 getinterval def color_packet 0 get 0.299 mul color_packet 1 get 0.587 mul add color_packet 2 get 0.114 mul add cvi /gray_packet exch def compression 0 gt { /number_pixels 1 def } { currentfile byte readhexstring pop 0 get /number_pixels exch 1 add def } ifelse 0 1 number_pixels 1 sub { pixels exch gray_packet put } for pixels 0 number_pixels getinterval } bind def /PseudoClassPacket { % % Get a PseudoClass packet. % % Parameters: % index: index into the colormap. % length: number of pixels minus one of this color (optional). % currentfile byte readhexstring pop 0 get /offset exch 3 mul def /color_packet colormap offset 3 getinterval def compression 0 gt { /number_pixels 3 def } { currentfile byte readhexstring pop 0 get /number_pixels exch 1 add 3 mul def } ifelse 0 3 number_pixels 1 sub { pixels exch color_packet putinterval } for pixels 0 number_pixels getinterval } bind def /PseudoClassImage { % % Display a PseudoClass image. % % Parameters: % class: 0-PseudoClass or 1-Grayscale. % currentfile buffer readline pop token pop /class exch def pop class 0 gt { currentfile buffer readline pop token pop /depth exch def pop /grays columns 8 add depth sub depth mul 8 idiv string def columns rows depth [ columns 0 0 rows neg 0 rows ] { currentfile grays readhexstring pop } image } { % % Parameters: % colors: number of colors in the colormap. % colormap: red, green, blue color packets. % currentfile buffer readline pop token pop /colors exch def pop /colors colors 3 mul def /colormap colors string def currentfile colormap readhexstring pop pop systemdict /colorimage known { columns rows 8 [ columns 0 0 rows neg 0 rows ] { PseudoClassPacket } false 3 colorimage } { % % No colorimage operator; convert to grayscale. % columns rows 8 [ columns 0 0 rows neg 0 rows ] { GrayPseudoClassPacket } image } ifelse } ifelse } bind def /DisplayImage { % % Display a DirectClass or PseudoClass image. % % Parameters: % x & y translation. % x & y scale. % label pointsize. % image label. % image columns & rows. % class: 0-DirectClass or 1-PseudoClass. % compression: 0-RunlengthEncodedCompression or 1-NoCompression. % hex color packets. % gsave currentfile buffer readline pop token pop /x exch def token pop /y exch def pop x y translate currentfile buffer readline pop token pop /x exch def token pop /y exch def pop currentfile buffer readline pop token pop /pointsize exch def pop /Helvetica findfont pointsize scalefont setfont x y scale currentfile buffer readline pop token pop /columns exch def token pop /rows exch def pop currentfile buffer readline pop token pop /class exch def pop currentfile buffer readline pop token pop /compression exch def pop class 0 gt { PseudoClassImage } { DirectClassImage } ifelse grestore } bind def %%EndProlog %%Page: 1 1 %%PageBoundingBox: 0 0 575 215 userdict begin %%BeginData: DisplayImage 0 0 576 216 12 576 216 1 1 1 1 ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff 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%%BoundingBox: 0 0 575 215 %%EOF %%EndDocument @endspecial 10060 39141 a Fr(Figure)417 b(5.)553 b Fs(Primary)370 b(homo)31 b(clinic)372 b(bifurcation)f(diagram)g(\(sc)-31 b(hematic\).)10060 40470 y Fn(\034)406 b Fs(represen)-31 b(ts)279 b(natural)j(parametarization)j(along)d(the)f(unstable)h (manifold.)6075 43524 y(and)540 b(w)-31 b(e)540 b(see)g(that)h Fn(k)35 b Fs(\()p Fn(r)c Fs(;)184 b Fn(\027)70 b Fs(\))542 b(c)-31 b(hanges)541 b(at)g Fn(\027)24717 43690 y Fo(1)25753 43524 y Fs(for)f(all)h Fn(k)627 b(>)592 b(j)r(;)540 b Fs(hence,)583 b(as)540 b(opp)31 b(osed)540 b(to)h(the)6075 44852 y Fn(r)6574 45018 y Ff(n)7177 44852 y Fs('s,)453 b(it)437 b(do)31 b(es)435 b(not)i(serv)-31 b(e)435 b(as)h(a)h(go)31 b(o)g(d)436 b(lab)31 b(eling)438 b(system)e(for)g(the)h(homo)31 b(clinic)438 b(orbits)f(across)6075 46181 y(bifurcations.)20801 48546 y(4.)554 b Fr(Lobes)419 b(topology)7403 50539 y Fs(Consider)413 b(no)-31 b(w)413 b(a)g(\014xed)f Fn(\027)483 b Fs(v)-61 b(alue,)424 b(with)413 b Fn(Lbl)22 b Fs(\()p Fn(\027)70 b Fs(\))381 b(=)f Fl(f)p Fn(r)30647 50705 y Fo(1)31144 50539 y Fn(;)184 b(r)32134 50705 y Fo(2)32632 50539 y Fn(;)g(:::;)g(r)35034 50705 y Fo(2)p Ff(n)36082 50539 y Fl(g)413 b Fs(where)f Fn(N)121 b Fs(\()p Fn(\027)70 b Fs(\))380 b(=)g(2)p Fn(n)p Fs(,)6075 51867 y(and)i Fn(p)8797 51283 y Ff(r)9208 51394 y Fi(2)p Fh(n)p Fi(+1)8797 52162 y Fo(0)11457 51867 y Fs(=)328 b Fn(F)154 b(p)14069 51375 y Ff(r)14480 51486 y Fi(1)14069 52162 y Fo(0)15296 51867 y Fs(=)328 b Fn(p)17042 51375 y Ff(r)17453 51486 y Fi(1)17042 52162 y Fo(1)17941 51867 y Fs(.)530 b(Henceforth)383 b(w)-31 b(e)382 b(omit)i(the)e(explicit)h(dep)31 b(endence)382 b(on)g Fn(\027)452 b Fs(unless)6075 53195 y(needed.)6075 55209 y Fg(De\014nition)425 b(2.)554 b Fn(p)14120 54808 y Ff(r)14610 55209 y Fn(;)184 b(p)15658 54808 y Ff(r)16093 54474 y Fc(0)16845 55209 y Fl(2)307 b Fn(P)154 b Fs(\()p Fn(\027)70 b Fs(\))397 b Fq(ar)-57 b(e)396 b(c)-57 b(al)57 b(le)-57 b(d)396 b(neighb)-57 b(ors)397 b(if)g Fl(j)p Fn(k)35 b Fs(\()p Fn(r)c Fs(\))248 b Fl(\000)e Fn(k)35 b Fs(\()p Fn(r)36754 54808 y Fk(0)37065 55209 y Fs(\))p Fl(j)308 b Fs(=)g(1)p Fn(:)6075 57326 y Fg(De\014nition)477 b(3.)580 b Fn(R)14491 56924 y Ff(r)14482 57600 y Fo(0)15417 57326 y Fq(and)437 b Fn(R)18458 56924 y Ff(r)18893 56590 y Fc(0)18449 57600 y Fo(0)19684 57326 y Fq(\(se)-57 b(e)437 b(\(3.1\)\))f(ar)-57 b(e)437 b(c)-57 b(al)57 b(le)-57 b(d)438 b(neighb)-57 b(oring)439 b(r)-57 b(e)g(gions)438 b(if)g Fn(p)41674 56924 y Ff(r)42164 57326 y Fn(;)184 b(p)43212 56924 y Ff(r)43647 56590 y Fc(0)44440 57326 y Fq(ar)-57 b(e)6075 58654 y(neighb)g(ors.)7403 60709 y Fs(The)320 b(di\013erence)g(b)31 b(et)-31 b(w)g(een)321 b(neigh)-31 b(b)31 b(oring)322 b(regions)e Fn(R)29301 60307 y Ff(r)29292 60984 y Fo(0)30111 60709 y Fs(and)g Fn(R)33064 60307 y Ff(r)33499 59973 y Fc(0)33055 60984 y Fo(0)34173 60709 y Fs(are)f(lob)31 b(es)321 b(-)f(regions)g(whic)-31 b(h)6075 62138 y(are)369 b(enclosed)g(b)-31 b(y)370 b(the)f(segmen)-31 b(ts)370 b Fn(U)121 b Fs([)p Fn(p)22197 61736 y Ff(r)22197 62412 y Fo(0)22694 62138 y Fn(;)184 b(p)23742 61736 y Ff(r)24177 61402 y Fc(0)23742 62412 y Fo(0)24532 62138 y Fs(])p Fl([)369 b Fn(S)64 b Fs([)p Fn(p)27553 61736 y Ff(r)27553 62412 y Fo(0)28050 62138 y Fn(;)184 b(p)29098 61736 y Ff(r)29533 61402 y Fc(0)29098 62412 y Fo(0)29889 62138 y Fs(]:)6075 64254 y Fg(De\014nition)346 b(4.)491 b Fq(A)332 b(lob)-57 b(e)333 b Fn(L)p Fs(\()p Fn(p)18459 63852 y Ff(r)18459 64542 y(i)18950 64254 y Fn(;)184 b(p)19998 63852 y Ff(r)20433 63518 y Fc(0)19998 64542 y Ff(i)20789 64254 y Fs(\))333 b Fq(is)g(the)f(r)-57 b(e)g(gion)334 b(enclose)-57 b(d)333 b(by)g Fn(@)61 b(L)308 b Fs(=)f Fn(U)121 b Fs([)p Fn(p)37975 63852 y Ff(r)37975 64542 y(i)38466 64254 y Fn(;)184 b(p)39514 63852 y Ff(r)39949 63518 y Fc(0)39514 64542 y Ff(i)40304 64254 y Fs(])p Fl([)333 b Fn(S)64 b Fs([)p Fn(p)43289 63852 y Ff(r)43289 64542 y(i)43779 64254 y Fn(;)184 b(p)44827 63852 y Ff(r)45262 63518 y Fc(0)44827 64542 y Ff(i)45618 64254 y Fs(])6075 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33261 y Fo(0)22743 32966 y Fn(;)184 b(p)23791 32366 y Ff(r)24202 32477 y Fh(j)23791 33261 y Fo(0)24671 32966 y Fs(\))308 b Fd(t)26147 33132 y Ff(T)27152 32966 y Fn(@)61 b(R)28651 32366 y Ff(r)29062 32477 y Fh(j)33 b Fi(+1)28642 33261 y Fo(0)30783 32966 y Fs(=)308 b Fl(;)p Fn(;)17825 35002 y(U)121 b Fs(\()p Fn(p)19689 34403 y Ff(r)20100 34514 y Fh(j)19689 35297 y Fo(0)20569 35002 y Fn(;)184 b(p)21617 34403 y Ff(r)22028 34514 y Fh(j)33 b Fi(+1)21617 35297 y Fo(0)23443 35002 y Fs(\))308 b Fd(t)24919 35168 y Ff(T)25924 35002 y Fn(S)64 b Fs(\()p Fn(p)27654 34403 y Ff(r)28065 34514 y Fh(j)33 b Fi(+1)27654 35297 y Fo(0)29479 35002 y Fn(;)184 b(p)30527 34403 y Ff(r)30938 34514 y Fh(j)30527 35297 y Fo(0)31408 35002 y Fs(\))308 b(=)f Fl(;)p Fn(:)6075 36679 y Fs(where)264 b Fd(t)9909 36845 y Ff(T)10871 36679 y Fs(denotes)h(top)31 b(ologically)269 b(transv)-31 b(erse)264 b(in)-31 b(tersection.)459 b(These)265 b(results,)285 b(together)266 b(with)6075 38008 y(the)425 b(observ)-61 b(ation)426 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Fs(or)508 b(is)h(completely)h(outside)g(of)f(it.)911 b(Hence,)544 b(either)509 b Fn(R)29742 40263 y Fo(1)29733 40939 y(0)30777 40664 y Fs(=)540 b Fn(R)33028 40263 y Fo(2)33019 40939 y(0)33862 40664 y Fl(])339 b Fn(E)35756 40830 y Fo(1)36761 40664 y Fs(or)509 b Fn(R)39107 40263 y Fo(2)39098 40939 y(0)40142 40664 y Fs(=)540 b Fn(R)42393 40263 y Fo(1)42384 40939 y(0)43227 40664 y Fl(])339 b Fn(E)45121 40830 y Fo(1)45618 40664 y Fs(.)6075 41993 y(Ho)-31 b(w)g(ev)g(er,)430 b(the)416 b(latter)i(con)-31 b(tradicts)418 b(the)f(c)-31 b(hoice)417 b(of)g Fn(R)29114 41591 y Fo(1)29105 42267 y(0)30026 41993 y Fs(as)f(the)h(region)g(with) g(maximal)j(area)6075 43321 y(as)431 b Fn(\027)482 b Fl(!)412 b Fs(0)10597 42919 y Fo(+)11332 43321 y Fs(.)681 b(Another)432 b(manifestation)j(of)d(the)g(lab)31 b(eling)434 b(sc)-31 b(heme)432 b(ma)-31 b(y)433 b(b)31 b(e)431 b(form)-31 b(ulated)434 b(b)-31 b(y)6075 44649 y(lo)31 b(oking)516 b(at)f(the)g(manifold's)i(orien)-31 b(tation:)785 b Fn(E)26282 44815 y Fo(1)27328 44649 y Fl(\032)550 b Fn(R)29589 44248 y Fo(1)29580 44924 y(0)30598 44649 y Fs(i\013)515 b Fn(U)121 b Fs([)p Fn(p)33807 44248 y Fo(1)33807 44924 y(0)34303 44649 y Fs(\()p Fn(\027)70 b Fs(\))p Fn(;)184 b(p)36828 44248 y Fo(2)36828 44924 y(0)37327 44649 y Fs(\()p Fn(\027)70 b Fs(\)])516 b(is)e(in)-31 b(terior)515 b(to)6075 45978 y Fn(S)64 b Fs([)p Fn(p)7682 45576 y Fo(1)7682 46252 y(0)8178 45978 y Fs(\()p Fn(\027)70 b Fs(\))p Fn(;)184 b(p)10703 45576 y Fo(2)10703 46252 y(0)11202 45978 y Fs(\()p Fn(\027)70 b Fs(\)])370 b(as)e(sho)-31 b(wn)369 b(in)f(\014gure)g(3.)493 b(The)368 b(manifolds)j(orien)-31 b(tation)371 b(is)d(clearly)h(preserv)-31 b(ed)6075 47306 y(for)393 b Fn(\027)419 b Fl(2)347 b Fs(\(0)p Fn(;)184 b(\027)11865 47472 y Fo(1)12364 47306 y Fs(\).)566 b(F)-92 b(urthermore,)399 b(b)-31 b(y)394 b(top)31 b(ological)397 b(transv)-31 b(ersalit)g(y)396 b(of)e(the)f(p)31 b(oin)-31 b(ts)395 b(in)e Fn(P)154 b Fs(\()p Fn(\027)70 b Fs(\))394 b(it)6075 48634 y(follo)-31 b(ws)380 b(immediately)h(that)e(all)g(o)31 b(dd)378 b(\(resp)31 b(ectiv)-31 b(ely)379 b(ev)-31 b(en\))379 b(indexed)f(p)31 b(oin)-31 b(ts)379 b(ha)-31 b(v)g(e)379 b(the)f(same)6075 49963 y(manifolds)430 b(orien)-31 b(tation)431 b(as)c(of)i Fn(p)20135 49561 y Fo(1)20135 50237 y(0)20631 49963 y Fs(\()p Fn(\027)70 b Fs(\))429 b(\(resp)31 b(ectiv)-31 b(ely)430 b Fn(p)29620 49561 y Fo(2)29620 50237 y(0)30116 49963 y Fs(\()p Fn(\027)70 b Fs(\)\),)445 b(so)427 b(that)j(for)e(0)405 b Fn(<)h(\027)475 b(<)406 b(\027)43464 50129 y Fo(1)44388 49963 y Fs(the)6075 51291 y(lemma)371 b(is)e(pro)-31 b(v)g(ed)369 b(for)h(all)g Fn(k)35 b Fs(.)7403 52619 y(F)-92 b(or)335 b Fn(\027)9903 52785 y Ff(j)10677 52619 y Fn(<)307 b(\027)378 b(<)307 b(\027)14485 52785 y Ff(j)45 b Fo(+1)16072 52619 y Fs(,)343 b(the)336 b(lemma)h(is)f(pro)-31 b(v)g(ed)336 b(b)-31 b(y)336 b(induction,)345 b(noticing)338 b(that)f(at)f(the)g(bifur-)6075 53948 y(cations,)499 b(top)31 b(ologically)477 b(transv)-31 b(erse)472 b(homo)31 b(clinic)474 b(p)31 b(oin)-31 b(ts)473 b(are)f(inserted/deleted)h(in)f (neigh-)6075 55276 y(b)31 b(oring)465 b(pairs,)489 b(hence)464 b(the)h(orien)-31 b(tation)467 b(of)e(the)g(manifolds)i(at)e Fn(p)34164 54685 y Ff(r)34575 54802 y Fi(2)p Fh(k)9 b Fi(+1)34164 55571 y Fo(0)36437 55276 y Fs(\()p Fn(\027)70 b Fs(\))465 b(\(resp)31 b(ectiv)-31 b(ely)466 b(at)6075 56604 y Fn(p)6632 56106 y Ff(r)7043 56223 y Fi(2)p Fh(k)6632 56900 y Fo(0)7959 56604 y Fs(\()p Fn(\027)70 b Fs(\)\))443 b(is)e(alw)-31 b(a)g(ys)443 b(as)f(that)g(of)g Fn(p)20900 56203 y Fo(1)20900 56879 y(0)21397 56604 y Fs(\(0)22380 56203 y Fo(+)23116 56604 y Fs(\))f(\(resp)31 b(ectiv)-31 b(ely)443 b(as)e(of)h Fn(p)33847 56203 y Fo(2)33847 56879 y(0)34344 56604 y Fs(\(0)35327 56203 y Fo(+)36063 56604 y Fs(\)\).)710 b(Notice)443 b(that)f(tan-)6075 57933 y(gen)-31 b(t,)370 b(non)g(top)31 b(ologically)374 b(transv)-31 b(erse)368 b(homo)31 b(clinic)372 b(p)31 b(oin)-31 b(ts)370 b(are)f(not)h(lab)31 b(eled.)5908 b Fd(\003)6075 60091 y Fg(Corollary)522 b(1.)595 b Fq(F)-85 b(or)459 b(al)57 b(l)459 b Fn(\027)493 b(>)423 b Fs(0)461 b Fq(the)e(r)-57 b(e)g(gions)461 b(with)e(even)i(or)-57 b(der)459 b(have)h(smal)57 b(ler)459 b(ar)-57 b(e)g(as)460 b(than)6075 61420 y(their)340 b(neighb)-57 b(ors,)353 b(namely)341 b Fn(R)18452 60829 y Ff(r)18863 60946 y Fi(2)p Fh(k)9 b Fi(+1)18443 61715 y Fo(0)21064 61420 y Fq(ar)-57 b(e)341 b(r)-57 b(e)g(gions)341 b(of)g(lo)-57 b(c)g(al)57 b(ly)341 b(maximal)f(ar)-57 b(e)g(a)341 b(wher)-57 b(e)g(as)340 b Fn(R)42774 60921 y Ff(r)43185 61038 y Fi(2)p Fh(k)42765 61715 y Fo(0)44440 61420 y Fq(ar)-57 b(e)6075 62748 y(r)g(e)g(gions)397 b(of)f(lo)-57 b(c)g(al)57 b(ly)397 b(minimal)g(ar)-57 b(e)g(as.)7403 64807 y Fs(Finally)-92 b(,)371 b(note)f(the)f(follo)-31 b(wing)373 b(prop)31 b(ert)-31 b(y)370 b(of)f(the)h(lob)31 b(es:)6075 66866 y Fg(Prop)k(osition)426 b(1.)554 b Fq(The)396 b(lob)-57 b(es)396 b Fn(E)20240 67032 y Ff(k)20785 66866 y Fn(;)184 b(D)22192 67032 y Ff(k)23134 66866 y Fn(k)343 b Fs(=)307 b(1)p Fn(;)184 b(:::;)g(N)121 b Fs(\()p Fn(\027)70 b Fs(\))401 b Fq(ar)-57 b(e)397 b(simply)f(c)-57 b(onne)g(cte)g(d.)p 6075 68221 6642 45 v 7403 69198 a Fo(3)7844 69541 y Fu(])314 b Fx(denotes)g(a)g(union)g(of)g(sets)g(with)f(disjoin)-26 b(t)314 b(in)-26 b(terior.)p eop %%Page: 10 10 10 9 bop 6075 3345 a Fo(10)14390 b(VERED)299 b(R)-24 b(OM-KED)g(AR.)6075 6001 y Fq(Pr)-57 b(o)g(of.)554 b Fs(The)590 b(lob)31 b(e's)590 b(b)31 b(oundaries,)646 b(b)-31 b(y)590 b(de\014nition,)647 b(are)589 b(giv)-31 b(en)591 b(b)-31 b(y)590 b Fn(U)121 b Fs(\()p Fn(p)37653 5402 y Ff(r)38064 5513 y Fh(j)37653 6297 y Fo(0)38533 6001 y Fs(\()p Fn(\027)70 b Fs(\))p Fn(;)184 b(p)41058 5402 y Ff(r)41469 5513 y Fh(j)33 b Fi(+1)41058 6297 y Fo(0)42886 6001 y Fs(\()p Fn(\027)70 b Fs(\)\))394 b Fl([)6075 7340 y Fn(S)64 b Fs(\()p Fn(p)7805 6741 y Ff(r)8216 6852 y Fh(j)7805 7636 y Fo(0)8685 7340 y Fs(\()p Fn(\027)70 b Fs(\))p Fn(;)184 b(p)11210 6741 y Ff(r)11621 6852 y Fh(j)33 b Fi(+1)11210 7636 y Fo(0)13037 7340 y Fs(\()p Fn(\027)70 b Fs(\)\),)463 b(whic)-31 b(h)444 b(are)e(b)31 b(oth)444 b(connected)f(arcs)f(whic)-31 b(h)444 b(are)e(joined)i(at)f (their)g(end-)6075 8669 y(p)31 b(oin)-31 b(ts,)480 b(hence)457 b(the)g(lob)31 b(es)458 b(are)f(connected.)757 b(Eac)-31 b(h)458 b(comp)31 b(onen)-31 b(t)458 b(of)g(the)g(b)31 b(oundary)457 b(cannot)6075 9997 y(in)-31 b(tersect)287 b(itself,)305 b(and)287 b(b)-31 b(y)287 b(lemma)i(1)e(they)g(cannot)h (in)-31 b(tersect)288 b(transv)-31 b(ersely)287 b(eac)-31 b(h)287 b(other)g(either,)6075 11326 y(so)377 b(the)h(only)g(source)f (of)h(non-trivial)i(top)31 b(ology)381 b(ma)-31 b(y)378 b(stem)g(from)g(tangencies.)519 b(The)378 b(app)31 b(ear-)6075 12654 y(ance)407 b(of)g(primary)h(homo)31 b(clinic)409 b(tangency)f(\(e.g.)607 b(at)408 b Fn(\027)441 b Fs(=)370 b Fn(\027)31387 12820 y Fo(1)32290 12654 y Fs(of)408 b(\014gure)e(4\))i(do)31 b(es)406 b(not)i(c)-31 b(hange)6075 13982 y(the)365 b(simple)h(connectedness)e(prop)31 b(ert)-31 b(y)365 b(of)h(a)f(lob)31 b(e.)492 b(Finally)-92 b(,)367 b(it)f(follo)-31 b(ws)367 b(from)e(eq.)492 b(\(4.2\))367 b(that)6075 15311 y(the)351 b(lob)31 b(e)351 b(cannot)h(reconnect)f (and)g(form)g(a)g(ring)g(\(ev)-31 b(en)352 b(in)f(the)g(closed)g (geometry)h(case!\).)1108 b Fd(\003)6075 17866 y Fs(4.2.)555 b Fg(Con)-35 b(tin)g(uous)399 b(dep)35 b(endence)400 b(on)e(parameters.)554 b Fs(F)-92 b(or)345 b(ev)-31 b(ery)345 b Fn(\027)416 b Fs(there)345 b(exist)h(a)g(collec-)6075 19194 y(tion)275 b(of)g(incoming)h(and)f(outgoing)h(lob)31 b(es.)461 b(Their)275 b(areas)f(c)-31 b(hanges)275 b(with)g Fn(\027)70 b Fs(,)294 b(and,)g(at)275 b(homo)31 b(clinic)6075 20522 y(bifurcation)434 b(p)31 b(oin)-31 b(ts)432 b(these)g(c)-31 b(hanges)433 b(can)f(b)31 b(e)431 b(discon)-31 b(tin)g(uous)434 b(\(at)f(ev)-31 b(en)432 b(order)f(bifurcations)6075 21851 y(where)369 b(lob)31 b(es)369 b(split)h(or)f(coincide,)i(as)e (sho)-31 b(wn)370 b(in)f(\014gure)g(4\).)494 b(Nonetheless,)6075 24068 y Fg(Prop)35 b(osition)529 b(2.)608 b Fq(Consider)479 b(a)f(fr)-57 b(e)g(quency-sp)g(anning)483 b(homo)-57 b(clinic)480 b(family.)759 b(The)479 b(sums)f(of)6075 25396 y(the)395 b(ar)-57 b(e)g(as)397 b(of)f(the)g(outgoing)792 b(and)396 b(inc)-57 b(oming)399 b(lob)-57 b(es:)6075 29047 y Fs(\(4.3\))9190 b Fn(\026)18205 29213 y Ff(D)19315 29047 y Fs(=)20616 27107 y Fh(N)60 b Fi(\()p Fh(\027)39 b Fi(\))p 20616 27320 1689 38 v 21272 27762 a(2)20661 27996 y Fj(X)20744 30353 y Ff(i)p Fo(=1)22622 29047 y Fn(\026)p Fs(\()p Fn(D)24635 29213 y Ff(i)25005 29047 y Fs(\))p Fn(;)977 b(\026)27386 29213 y Ff(E)28442 29047 y Fs(=)29743 27107 y Fh(N)60 b Fi(\()p Fh(\027)39 b Fi(\))p 29743 27320 V 30399 27762 a(2)29788 27996 y Fj(X)29870 30353 y Ff(i)p Fo(=1)31749 29047 y Fn(\026)p Fs(\()p Fn(E)33663 29213 y Ff(i)34032 29047 y Fs(\))6075 32334 y Fq(ar)-57 b(e)396 b Fn(C)8826 31933 y Fo(1)9719 32334 y Fq(in)h Fn(\027)9 b(:)6075 34552 y Fq(Pr)-57 b(o)g(of.)554 b Fs(It)466 b(follo)-31 b(ws)468 b(from)f(lemma)g(1)g(that)g(a)-31 b(w)g(a)g(y)468 b(of)e(the)g(primary)h(homo)31 b(clinic)468 b(bifurcation)6075 35880 y(v)-61 b(alues)519 b Fl(f)p Fn(\027)10621 36046 y Ff(i)10990 35880 y Fl(g)11543 35479 y Fk(1)11543 36168 y Ff(i)p Fo(=1)13552 35880 y Fs(the)g(area)h(of)g (eac)-31 b(h)520 b(lob)31 b(e)519 b(dep)31 b(ends)519 b(smo)31 b(othly)521 b(\()p Fn(C)35413 35479 y Ff(r)35904 35880 y Fs(\))f(on)f Fn(\027)70 b Fs(,)558 b(hence)519 b(so)g(do)6075 37209 y Fn(\026)6742 37375 y Ff(D)8120 37209 y Fs(and)575 b Fn(\026)11145 37375 y Ff(E)11893 37209 y Fs(.)1111 b(By)575 b(orien)-31 b(tation)578 b(preserv)-61 b(ation,)627 b(near)575 b(the)h(bifurcation)h(v)-61 b(alues)575 b(an)h(ev)-31 b(en)6075 38537 y(n)g(um)g(b)31 b(er)509 b(of)i(top)31 b(ological)513 b(transv)-31 b(erse)510 b(primary)g(homo)31 b(clinic)512 b(p)31 b(oin)-31 b(ts)510 b(are)g(added)g(or)f(elimi-)6075 39865 y(nated.)491 b(Consider)362 b(\014rst)g(a)h(tangen)-31 b(tial)365 b(bifurcation)f(of)f(ev)-31 b(en)362 b(order)g(o)31 b(ccurring)362 b(at)h 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Fo(1)13351 45179 y Fs(\))g(\(enclosed)g(b)-31 b(y)442 b Fn(U)121 b Fs([)p Fn(p)22451 44777 y Fo(2)p Ff(j)23359 45179 y Fn(;)184 b(p)24407 44777 y Fo(2)p Ff(j)45 b Fo(+1)26436 45179 y Fs(])295 b Fl([)g Fn(S)64 b Fs([)p Fn(p)29678 44777 y Fo(2)p Ff(j)45 b Fo(+1)31706 45179 y Fn(;)184 b(p)32754 44777 y Fo(2)p Ff(j)33663 45179 y Fs(]\))442 b(to)h(the)g(2)p Fn(n)295 b Fs(+)g(1)442 b(disjoin)-31 b(t)45482 44750 y Fo(5)6075 46507 y Fs(lob)31 b(es)319 b Fn(D)9745 46673 y Ff(j)10212 46507 y Fs(\()p Fn(\027)70 b Fs(\))p Fn(;)184 b(E)12997 46673 y Ff(j)45 b Fo(+1)14586 46507 y Fs(\()p Fn(\027)70 b Fs(\))p Fn(;)184 b(D)17470 46673 y Ff(j)45 b Fo(+1)19060 46507 y Fs(\()p Fn(\027)70 b Fs(\))p Fn(;)184 b(:::;)g(E)23257 46673 y Ff(j)45 b Fo(+)p Ff(n)24955 46507 y Fs(\()p Fn(\027)70 b Fs(\))p Fn(;)184 b(D)27839 46673 y Ff(j)45 b Fo(+)p Ff(n)29535 46507 y Fs(\()p Fn(\027)70 b Fs(\))320 b(created)g(b)-31 b(y)319 b(the)g(new)h(homo)31 b(clinic)6075 47888 y(p)g(oin)-31 b(ts.)604 b(As)406 b Fn(\027)439 b Fl(!)369 b Fn(\027)14695 47414 y Fo(+)14625 48222 y Ff(k)15430 47888 y Fn(;)406 b Fs(b)-31 b(y)406 b(the)h(smo)31 b(oth)407 b(dep)31 b(endence)405 b(of)i(the)f(manifolds)i(on)e Fn(\027)477 b Fs(\(recall)407 b(that)6075 49216 y(only)284 b(a)f(\014nite)h (extension)g(of)g(the)f(lo)31 b(cal)285 b(stable)f(and)f(unstable)h (manifolds)h(is)e(considered)g(here\),)6075 50544 y(the)298 b(areas)g(of)g(the)g(in)-31 b(terior,)314 b(newly)298 b(created)g(lob)31 b(es)298 b(\()p Fn(E)28744 50710 y Ff(j)45 b Fo(+1)30332 50544 y Fs(\()p Fn(\027)70 b Fs(\))p Fn(;)184 b(:::;)g(E)34529 50710 y Ff(j)45 b Fo(+)p Ff(n)36227 50544 y Fs(\()p Fn(\027)70 b Fs(\)\))300 b(v)-61 b(anish,)312 b(whereas)6075 51873 y Fn(\026)p Fs(\()p Fn(D)8088 52039 y Ff(j)8555 51873 y Fs(\()p Fn(\027)70 b Fs(\)\))251 b(+)f Fn(:::)h Fs(+)f Fn(\026)p Fs(\()p Fn(D)16120 52039 y Ff(j)45 b Fo(+)p Ff(n)17814 51873 y Fs(\()p Fn(\027)70 b Fs(\)\))318 b Fl(!)21146 52220 y Ff(\027)52 b Fk(!)p Ff(\027)23020 51860 y Fi(+)22968 52460 y(1)24016 51873 y Fn(\026)p Fs(\()p Fn(D)26029 52039 y Ff(j)26496 51873 y Fs(\()p Fn(\027)27473 52039 y Fo(1)27970 51873 y Fs(\)\).)510 b(The)375 b(area)g(of)g(the)g(diminishing)i(lob)31 b(es)6075 53553 y(near)476 b Fn(\027)9192 53719 y Ff(k)10214 53553 y Fs(is)g(of)i(the)f(form)g(\()p Fn(\027)389 b Fl(\000)318 b Fn(\027)20633 53719 y Ff(k)21177 53553 y Fs(\))21607 53152 y Ff(N)83 b Fo(+1)p Ff(=)-48 b(N)25235 53553 y Fs(where)953 b Fn(N)598 b Fs(is)477 b(the)g(order)f(of)i(the)f (tangency)h(at)6075 54882 y Fn(\027)6622 55048 y Ff(k)7166 54882 y Fs(.)484 b(Clearly)343 b(the)f(same)g(argumen)-31 b(t)343 b(applies)g(to)f(the)g(case)g(where)g(pairs)f(of)i(homo)31 b(clinic)344 b(orbits)6075 56210 y(annihilate)355 b(at)e Fn(\027)13107 56376 y Ff(k)13651 56210 y Fn(:)g Fs(It)f(follo)-31 b(ws)355 b(that)f(generically)g Fn(\026)p Fs(\()p Fn(D)31 b Fs(\))353 b(and)g Fn(\026)p Fs(\()p Fn(E)64 b Fs(\))353 b(are)f Fn(C)37408 55808 y Fo(1)38257 56210 y Fs(in)h Fn(\027)422 b Fs(\(I)352 b(thank)i(B.)6075 57538 y(Fiedler)369 b(for)g(this)h(observ)-61 b(ation\).)25148 b Fd(\003)7403 60093 y Fs(In)-31 b(tuitiv)g(ely)-92 b(,)483 b(w)-31 b(e)458 b(think)g(of)g(the)g Fn(D)22097 60259 y Ff(k)23099 60093 y Fs(lob)31 b(es)458 b(as)f(existing)i(lob)31 b(es)457 b(and)h(the)g Fn(E)39568 60259 y Ff(k)40570 60093 y Fs(as)f(en)-31 b(tering)6075 61422 y(lob)31 b(es.)466 b(A)290 b(more)g(elegan)-31 b(t)292 b(framew)-31 b(ork)292 b(for)e(discussing)g(transp)31 b(ort)290 b(in)g(phase)g(space)g(is)g(ac)-31 b(hiev)g(ed)6075 62750 y(b)g(y)369 b(in)-31 b(tro)31 b(ducing)371 b(the)e(notion)i(of)f (exit)g(and)g(en)-31 b(try)369 b(sets)g(\(see)g([12)q(],)h([13)r(]\):)p 6075 64833 6642 45 v 7403 65809 a Fo(4)7844 66152 y Fx(The)304 b(other)g(case,)j(of)d(homo)26 b(clinic)306 b(bifurcation)e(o)26 b(ccuring)305 b(b)26 b(et)-26 b(w)g(een)304 b(the)f(homo)26 b(clinic)307 b(p)26 b(oin)-26 b(ts)304 b Fv(p)42048 65840 y Ft(2)p Fe(j)39 b Fb(\000)p Ft(1)43933 66152 y Fv(;)157 b(p)44825 65840 y Ft(2)p Fe(j)45664 66152 y Fx(,)6075 67259 y(is)352 b(similar:)496 b(simply)352 b(c)-26 b(hange)353 b(the)e(corresp)26 b(onding)353 b(indices)f(and)g(in)-26 b(terc)g(hange)352 b(the)g(letters)g Fv(E)401 b Fx(and)351 b Fv(D)378 b Fx(in)352 b(this)6075 68366 y(paragraph.)7403 69198 y Fo(5)7844 69541 y Fx(b)-26 b(y)313 b(smo)26 b(othness)315 b(of)f(the)f(manifolds)p eop %%Page: 11 11 11 10 bop 10902 3345 a Fm(FREQUENCY)389 b(SP)-101 b(ANNING)388 b(HOMOCLINIC)f(F)-135 b(AMILIES.)4333 b Fo(11)6075 6001 y Fg(De\014nition)312 b(5.)465 b Fq(F)-85 b(or)305 b(any)h(r)-57 b(e)g(gion)307 b Fn(R)9 b Fq(,)323 b(the)305 b(exit)g(\()p Fn(D)27237 6167 y Ff(R)27963 6001 y Fq(\))h(and)f(entry)h(\()p Fn(E)34860 6167 y Ff(R)35586 6001 y Fq(\))f(sets)f(of)i Fn(R)314 b Fq(ar)-57 b(e)305 b(de\014ne)-57 b(d)6075 7330 y(as:)18028 8703 y Fn(D)18944 8869 y Ff(R)19978 8703 y Fs(=)p 21146 7740 4306 45 v 307 w Fn(R)9 b Fl(n)p Fn(F)23415 8383 y Fk(\000)p Fo(1)24603 8703 y Fn(R)f(;)1769 b(E)28345 8869 y Ff(R)29379 8703 y Fs(=)p 30547 7740 3118 45 v 307 w Fn(R)9 b Fl(n)p Fn(F)154 b(R)8 b(:)7403 10721 y Fs(In)408 b(app)31 b(endix)408 b(2)h(w)-31 b(e)408 b(study)g(the)h(relation)h(b)31 b(et)-31 b(w)g(een)409 b(en)-31 b(try)408 b(and)g(exit)h(sets)f(of)g(the)h(regions)6075 12049 y Fn(R)6925 11450 y Ff(r)7336 11561 y Fh(j)6916 12345 y Fo(0)8172 12049 y Fs(and)369 b(the)g(corresp)31 b(onding)368 b(en)-31 b(tering)370 b(and)f(exiting)h(lob)31 b(es.)493 b(In)368 b(particular,)i(w)-31 b(e)369 b(de\014ne,)g(for)6075 13388 y(eac)-31 b(h)359 b(region)h Fn(R)12719 12789 y Ff(r)13130 12900 y Fh(j)12710 13684 y Fo(0)13957 13388 y Fs(the)f(set)g(of)h(turnstile)g(lob)31 b(es)359 b Fn(E)26924 12987 y Ff(j)27391 13388 y Fn(;)184 b(D)28829 12987 y Ff(j)29953 13388 y Fs(in)360 b(terms)f(of)g(union)h(of)g(en)-31 b(tering)360 b(and)6075 14717 y(exiting)351 b(lob)31 b(es)350 b(\(see)f(equations)i(\(9.6\))h(in)e(the)f(app)31 b(endix\).)488 b(W)-92 b(e)348 b(conclude)i(that)h(in)f(case)f(there) 6075 16045 y(are)451 b(no)i(in)-31 b(tersections)453 b(b)31 b(et)-31 b(w)g(een)453 b(these)f(t)-31 b(w)g(o)453 b(sets)f(they)g(corresp)31 b(ond)451 b(exactly)j(to)f(the)f(en)-31 b(try)6075 17373 y(and)342 b(exit)i(sets)e(of)h Fn(R)14579 16774 y Ff(r)14990 16885 y Fh(j)14570 17669 y Fo(0)15458 17373 y Fs(.)483 b(Ho)-31 b(w)g(ev)g(er,)350 b(if)343 b(suc)-31 b(h)342 b(in)-31 b(tersections)344 b(exist,)349 b(the)343 b(t)-31 b(w)g(o)344 b(sets)e(are)g(di\013eren)-31 b(t.)6075 18702 y(W)-92 b(e)356 b(pro)-31 b(vide)357 b(an)g(example)h(whic)-31 b(h)357 b(demonstrates)h(that)g(when)f(suc) -31 b(h)356 b(in)-31 b(tersections)358 b(exist)f(the)6075 20030 y(measure)369 b(of)h(the)f(en)-31 b(try)369 b(and)h(exit)g(sets)f (dep)31 b(ends)368 b(on)h Fn(j)r(:)7403 21359 y Fq(We)396 b(ther)-57 b(efor)g(e)397 b(c)-57 b(onclude)397 b(that)e(while)h(the)g (notion)g(of)g(entry)h(and)f(exit)g(sets)f(app)-57 b(e)g(ars)396 b(mor)-57 b(e)6075 22687 y(ele)g(gant,)384 b(it)c(has)e(a)i(major)f (\015aw)g(fr)-57 b(om)380 b(a)f(dynamic)i(p)-57 b(oint)380 b(of)g(view)g(-)f(it)h(is)g(not)f(invariant)i(with)6075 24015 y(r)-57 b(esp)g(e)g(ct)397 b(to)e(the)h(r)-57 b(e)g(gions)397 b(de\014nition.)7403 25344 y Fs(Another)473 b(problem)f(arising)h(from) g(the)f(de\014nition)i(of)f(the)f(en)-31 b(try)472 b(and)h(exit)g(sets) e(has)h(to)6075 26672 y(do)511 b(with)i(self)e(in)-31 b(tersection)513 b(of)f(the)g(lob)31 b(es)511 b(\(for)h(close)g (geometry)-92 b(,)549 b(in)511 b(the)h(limit)i(of)e(highly)6075 28000 y(stretc)-31 b(hed)368 b(lob)31 b(es\).)493 b(Indeed,)369 b(the)f(b)31 b(oundaries)369 b(of)g(the)g(en)-31 b(try)368 b(and)h(exit)g(sets)f(ma)-31 b(y)370 b(dep)31 b(end)368 b(on)6075 29329 y(the)332 b(app)31 b(earance)333 b(of)g(non-primary)g (homo)31 b(clinic)335 b(orbits.)481 b(The)332 b(app)31 b(earance)333 b(of)g(suc)-31 b(h)331 b(orbits)i(is)6075 30657 y(exp)31 b(ected)384 b(to)h(dep)31 b(end)383 b(sensitiv)-31 b(ely)386 b(on)e(parameter)g(v)-61 b(alues.)537 b(Equiv)-61 b(alen)-31 b(tly)-92 b(,)391 b(the)384 b(prop)31 b(osition)6075 31985 y(regarding)338 b(the)f(smo)31 b(oth)339 b(dep)31 b(endence)336 b(of)i(the)f(lob)31 b(es)338 b(area)f(on)h(parameters)g (is)f(pro)-31 b(v)g(ed)337 b(for)h(the)6075 33314 y(sum)293 b(of)h(their)g(areas,)309 b Fn(\026)15851 33480 y Ff(E)16892 33314 y Fs(\(see)293 b(4.3\),)311 b(and)294 b(not)g(for)f(the)h(area)g (of)g(the)g(lob)31 b(es)293 b(union.)468 b(In)293 b(fact,)310 b(an)-31 b(y)6075 34642 y(de\014nition)402 b(of)f(\015ux)f(whic)-31 b(h)402 b(dep)31 b(ends)399 b(on)i(homo)31 b(clinic)403 b(orbits)d(of)h(higher)g(order)f(\(namely)i(not)6075 35970 y(primary)325 b(homo)31 b(clinic)327 b(orbits\))e(m)-31 b(ust)326 b(b)31 b(e)324 b(carefully)i(examined)g(due)e(to)h(the)g (recen)-31 b(t)325 b(results)f(on)6075 37299 y(Ric)-31 b(hness)368 b(of)i(c)-31 b(haos)370 b([23)q(])g(in)f(the)h(neigh)-31 b(b)31 b(orho)g(o)g(d)370 b(of)g(a)f(homo)31 b(clinic)372 b(tangency)-92 b(.)7403 38627 y(Hence,)488 b(w)-31 b(e)465 b(de\014ne)f(the)g(\015ux)g(in)-31 b(to)466 b(a)f(region)f(using)h(the) f(concept)h(of)g(the)f(sum)g(of)h(lob)31 b(es)6075 39955 y(areas:)6075 41974 y Fg(De\014nition)465 b(6.)574 b Fq(Consider)428 b(a)g(fr)-57 b(e)g(quency)431 b(sp)-57 b(anning)429 b(homo)-57 b(clinic)429 b(family.)607 b(The)511 b Fs(scaled)404 b(\015ux)6075 43302 y(function)370 b Fq(of)397 b(this)e(family)j(is:)6075 46604 y Fs(\(4.4\))p 16979 45641 3386 45 v 8631 w Fn(f)17521 46770 y Ff(l)t(ux)18886 46604 y Fs(\()p Fn(\027)70 b Fs(\))309 b(=)p 21973 44892 2208 45 v 21973 45855 a Fn(!)40 b Fs(\()p Fn(\027)70 b Fs(\))p 21973 46349 V 22465 47363 a(2)p Fn(\031)p 24313 45995 1415 45 v 24313 46604 a(\026)24980 46770 y Ff(E)26035 46604 y Fs(=)p 27337 44892 2208 45 v 27337 45855 a Fn(!)40 b Fs(\()p Fn(\027)70 b Fs(\))p 27337 46349 V 27828 47363 a(2)p Fn(\031)29994 44663 y Fh(N)60 b Fi(\()p Fh(\027)39 b Fi(\))p 29994 44877 1689 38 v 30650 45319 a(2)30039 45552 y Fj(X)30121 47910 y Ff(i)p Fo(=1)p 32000 45641 2714 45 v 32000 46604 a Fn(\026)p Fs(\()p Fn(E)33914 46770 y Ff(i)34283 46604 y Fs(\))p Fn(:)6075 49590 y Fg(Corollary)379 b(2.)503 b Fq(The)345 b(\015ux)f(function)i(of)f(a)g (fr)-57 b(e)g(quency)347 b(sp)-57 b(anning)347 b(homo)-57 b(clinic)346 b(family)g(dep)-57 b(ends)6075 50918 y(c)g(ontinuously)537 b(and)f(has)f(a)g(c)-57 b(ontinuous)537 b(derivative)g(\(is)e Fn(C)31700 50517 y Fo(1)32197 50918 y Fq(\))h(in)h(the)e(fr)-57 b(e)g(quency)539 b(sp)-57 b(anning)6075 52247 y(p)g(ar)g(ameter.)6075 54265 y(Pr)g(o)g(of.)554 b Fs(By)369 b(prop)31 b(osition)371 b(2)f(and)f(assumptions)h(A3)g(and)g(A7.)13001 b Fd(\003)7403 56321 y Fs(Notice)460 b(that)f(the)f(scaled)h(system)f(de\014nes)g(a)g (scaled)g(\015ux)h(function.)760 b(Substituting)461 b(the)6075 57650 y(scaling)337 b(function,)344 b(w)-31 b(e)336 b(observ)-31 b(e)336 b(that)h(the)f(\015ux)g(function)h(is)f(scaled)g(b)-31 b(y)336 b(the)g(t)-31 b(ypical)338 b(area)e(and)6075 58978 y(time)370 b(scale)g(asso)31 b(ciated)370 b(with)g(tra)-31 b(v)g(elling)373 b(along)e(the)e(homo)31 b(clinic)372 b(lo)31 b(op,)370 b(as)f(appropriate:)p 10020 60712 1908 45 v 10020 61614 a Fn(f)10562 61780 y Ff(l)t(ux)11927 61614 y Fs(\()p Fn(\027)70 b Fs(\))309 b(=)p 15014 59902 2208 45 v 15014 60865 a Fn(!)40 b Fs(\()p Fn(\027)70 b Fs(\))p 15014 61359 V 15506 62373 a(2)p Fn(\031)17354 61614 y(\026)p Fs(\()p 18451 60651 2360 45 v Fn(E)64 b Fs(\()p Fn(\027)70 b Fs(\))r(\))308 b(=)22850 60865 y Fn(L)23603 61031 y Fo(max)25292 60865 y Fs(\()p Fn(\027)70 b Fs(\))p 22850 61359 3921 45 v 23300 62373 a Fn(W)24345 62539 y Fo(0)24842 62373 y Fs(\()p Fn(\027)g Fs(\))28120 60865 y Fn(f)28662 61031 y Ff(l)t(ux)30027 60865 y Fs(\()p Fn(\027)g Fs(\))p 27036 61359 5553 45 v 27036 62373 a Fn(L)27789 62539 y Ff(x)28347 62373 y Fs(\()p Fn(\027)g Fs(\))p Fn(L)30577 62539 y Ff(y)31111 62373 y Fs(\()p Fn(\027)g Fs(\))33029 61614 y(=)35319 60865 y Fn(\034)35803 61031 y Ff(l)t(oop)p 34331 61359 4131 45 v 34331 62373 a Fn(Ar)31 b(ea)36791 62539 y Ff(l)t(oop)38594 61614 y Fn(f)39136 61780 y Ff(l)t(ux)40501 61614 y Fs(\()p Fn(\027)70 b Fs(\))13931 64615 y(5.)555 b Fr(Non-monotonicity)416 b(of)h(the)i(flux)f(function)6075 66607 y Fg(Theorem)312 b(1.)465 b Fq(Consider)306 b(a)f(fr)-57 b(e)g(quency-sp)g(anning)310 b(homo)-57 b(clinic)307 b(family.)481 b(Then,)324 b(in)307 b(the)e(sc)-57 b(ale)g(d)6075 67936 y(system)433 b(\(2.6\))g(the)g(sc) -57 b(ale)g(d)434 b(\015ux)e(function)j(\(e)-57 b(q)434 b(\(4.4\)\))f(dep)-57 b(ends)433 b(non-monotonic)-57 b(al)57 b(ly)435 b(on)f(the)6075 69264 y(sc)-57 b(ale)g(d)396 b(fr)-57 b(e)g(quency)399 b Fn($)31 b Fs(\()p Fn(\027)70 b Fs(\))p Fn(:)p eop %%Page: 12 12 12 11 bop 6075 3345 a Fo(12)14390 b(VERED)299 b(R)-24 b(OM-KED)g(AR.)6075 6001 y Fq(Pr)-57 b(o)g(of.)554 b Fs(Recall)383 b(that)h(b)-31 b(y)382 b(corollary)i(2)e(the)g(\015ux)g (function)i(dep)31 b(ends)381 b(con)-31 b(tin)g(uously)384 b(on)f Fn(\027)452 b Fs(and)6075 7634 y(that)p 8476 6670 3386 45 v 373 w Fn(f)9018 7800 y Ff(l)t(ux)10383 7634 y Fs(\()p Fn(\027)70 b Fs(\))314 b(=)p 13480 6403 1773 38 v 13480 7097 a Ff(!)28 b Fo(\()p Ff(\027)52 b Fo(\))p 13480 7379 1773 45 v 13873 8015 a(2)p Ff(\031)p 15386 7024 1415 45 v 15386 7634 a Fn(\026)16053 7800 y Ff(E)16800 7634 y Fn(:)373 b Fs(As)f Fn(\027)382 b Fl(!)313 b Fs(0,)373 b(the)g(system)f(\(2.6\))i(approac)-31 b(hes)373 b(the)g(adiabatic)h (limit.)6075 9007 y(Then,)529 b(b)-31 b(y)498 b(corollary)g(4)g(of)f (App)31 b(endix)497 b(2,)1027 b Fn(\026)26007 9173 y Ff(E)26755 9007 y Fs(\()p Fn(\027)70 b Fs(\))522 b Fl(!)e Fn(\026)31048 9173 y Ff(E)31796 9007 y Fs(\(0)32779 8606 y Fo(+)33515 9007 y Fs(\))h Fn(>)f Fs(0,)530 b(whic)-31 b(h)498 b(implies,)531 b(b)-31 b(y)6075 10446 y(assumption)303 b(A3)f(and)g(A7,)316 b(that)p 19969 9483 3904 45 v 303 w Fn(f)20511 10612 y Ff(f)87 b(l)t(ux)22395 10446 y Fs(\()p Fn(\027)70 b Fs(\))309 b Fl(!)e Fs(0.)470 b(F)-92 b(urthermore,)315 b(since)302 b Fn(\027)36791 10612 y Fo(1)37589 10446 y Fs(\(the)g(\014rst)g(primary)6075 11775 y(homo)31 b(clinic)417 b(bifurcation)g(v)-61 b(alue\))416 b(is)e(b)31 b(ounded)415 b(a)-31 b(w)g(a)g(y)417 b(from)f(zero,)426 b(it)416 b(follo)-31 b(ws)417 b(from)e(A3)h(that)6075 13214 y(there)499 b(exists)h(a)g(0)526 b Fn(<)557 b Fj(b)-647 b Fn(\027)595 b(<)525 b(\027)18817 13380 y Fo(1)19813 13214 y Fs(suc)-31 b(h)500 b(that)p 24970 12251 V 501 w Fn(f)25512 13380 y Ff(f)87 b(l)t(ux)27395 13214 y Fs(\()32 b Fj(b)-647 b Fn(\027)71 b Fs(\))526 b Fl(6)p Fs(=)f(0)500 b(and)p 34121 12251 V 500 w Fn(f)34663 13380 y Ff(f)87 b(l)t(ux)36546 13214 y Fs(\()p Fn(\027)70 b Fs(\))501 b(is)f(monotone)i(in)6075 14542 y(the)521 b(in)-31 b(terv)-61 b(al)523 b(\(0)p Fn(;)218 b Fj(b)-649 b Fn(\027)72 b Fs(].)950 b(On)522 b(the)f(other)h(hand,)560 b(as)522 b Fn($)31 b Fs(\()p Fn(\027)70 b Fs(\))562 b Fl(!)f(1)p Fs(,)f(a)-31 b(v)g(eraging)524 b(of)e(the)g(scaled)6075 15870 y(system)390 b(\(2.6\))j(implies)e(that)g(the)g(separatrix)g (splitting)h(is)e(exp)31 b(onen)-31 b(tially)394 b(small)d(in)g(1)p Fn(=$)31 b Fs(\()p Fn(\027)70 b Fs(\))6075 17199 y(\(see)521 b([17)r(],[14)r(],[5)r(]\).)951 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27466 19375 V -56 x Fn(f)28008 20504 y Ff(f)87 b(l)t(ux)29891 20338 y Fs(\()p Fn(\027)70 b Fs(\))31370 19065 y Fj(\014)31370 19729 y(\014)31370 20394 y(\014)32046 20338 y Fn(<)359 b(f)33808 20504 y Ff(f)87 b(l)t(ux)35692 20338 y Fs(\()32 b Fj(b)-647 b Fn(\027)70 b Fs(\).)490 b(This)359 b(pro)-31 b(v)g(es)360 b(that)p 6075 21257 V 6075 22220 a Fn(f)6617 22386 y Ff(f)87 b(l)t(ux)8500 22220 y Fs(\()p Fn(\027)70 b Fs(\))371 b(is)e(non-monotone)i(in)f Fn(\027)9 b(:)24192 b Fd(\003)7403 24258 y Fs(W)-92 b(e)254 b(no)-31 b(w)256 b(discuss)e(some)i(of)f(the)g(implications)j(of)e(the)f(non-monotone)j (b)31 b(eha)-31 b(vior)255 b(of)h(the)f(\015ux)6075 25587 y(function,)299 b(see)279 b([18)q(])h(for)f(a)h(\015uid)f(mixing)i (application)i(of)d(these)f(results.)462 b(First,)298 b(w)-31 b(e)279 b(notice)i(that)6075 26915 y(in)340 b(the)g(near-in)-31 b(tegrable)342 b(case,)k(when)341 b(the)f(n)-31 b(um)g(b)31 b(er)340 b(of)g(primary)h(homo)31 b(clinic)342 b(orbits)f(is)f (\014xed,)6075 28244 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y Fs(\()p Fn(\027)24055 43568 y Ff(b)24500 43402 y Fs(\))369 b(and)h Fn($)31 b Fs(\()p Fn(\027)29377 43568 y Ff(a)29912 43402 y Fs(\))677 b Fn(<)307 b($)31 b Fs(\()p Fn(\027)34112 43568 y Ff(b)34557 43402 y Fs(\))369 b(.)6075 45227 y(It)g(follo)-31 b(ws)371 b(immediately)-92 b(,)373 b(b)-31 b(y)370 b(the)f(\015ux)g (de\014nition,)j(that)p 21765 46139 3359 45 v 21765 47102 a Fn(\026)22432 47268 y Ff(E)23180 47102 y Fs(\()p Fn(\027)24157 47268 y Ff(a)24692 47102 y Fs(\))308 b Fn(>)p 26599 46139 3637 45 v 308 w(\026)27266 47268 y Ff(E)28014 47102 y Fs(\()p Fn(\027)28991 47268 y Ff(b)29436 47102 y Fs(\))6075 48927 y(namely)-92 b(,)496 b(the)469 b(sum)h(of)g(the)f(lob)31 b(es)470 b(areas)f(of)h(the)g(lo)-31 b(w)g(er)470 b(frequency)g(is)f (larger)h(than)g(that)h(of)6075 50255 y(the)385 b(higher)g(frequency) -92 b(.)540 b(This)385 b(observ)-61 b(ation,)391 b(whic)-31 b(h)386 b(is)f(w)-31 b(ell)386 b(re\015ected)f(when)g(one)g(examines) 6075 51584 y(P)-31 b(oincar)g(\023)-523 b(e)373 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Fl(\000)-185 b(!)27144 67882 y Ff($)24 b Fk(!)p Fo(0)29591 67716 y Fn(\026)p Fs(\()p Fn(E)31569 67258 y Ff(j)32035 67716 y Fs(\))6075 69541 y(where)369 b Fn(E)10157 69139 y Ff(j)10623 69541 y Fn(;)184 b(D)12061 69139 y Ff(j)12898 69541 y Fs(are)369 b(de\014ned)g(b)-31 b(y)369 b(eq.)493 b(\(9.6\))371 b(in)f(app)31 b(endix)369 b(2.)p eop %%Page: 13 13 13 12 bop 10902 3345 a Fm(FREQUENCY)389 b(SP)-101 b(ANNING)388 b(HOMOCLINIC)f(F)-135 b(AMILIES.)4333 b Fo(13)15289 6001 y Fs(6.)555 b Fr(F)-32 b(or)-25 b(ced)418 b(Saddle-center)j(bifur)-25 b(ca)-74 b(tion:)7403 7994 y Fs(As)369 b(an)g(example)i(consider)e(the) g(forced)h(saddle)f(cen)-31 b(ter)369 b(bifurcation:)20467 9177 y Ff(:)20282 9875 y Fn(x)307 b Fs(=)h Fn(p)20505 11030 y Ff(:)20358 11728 y Fn(p)f Fs(=)h Fn(\027)316 b Fl(\000)246 b Fn(x)24994 11271 y Fo(2)25736 11728 y Fs(+)g Fn(bx)27951 11271 y Ff(n)28738 11728 y Fs(sin)185 b Fn(!)40 b(t:)6075 13732 y Fs(F)-92 b(or)438 b(0)424 b Fn(<)g(\027)494 b Fl(\034)424 b Fs(1.)702 b(Near)439 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/GrayDirectClassPacket { % % Get a DirectClass packet; convert to grayscale. % % Parameters: % red % green % blue % length: number of pixels minus one of this color (optional). % currentfile color_packet readhexstring pop pop color_packet 0 get 0.299 mul color_packet 1 get 0.587 mul add color_packet 2 get 0.114 mul add cvi /gray_packet exch def compression 0 gt { /number_pixels 1 def } { currentfile byte readhexstring pop 0 get /number_pixels exch 1 add def } ifelse 0 1 number_pixels 1 sub { pixels exch gray_packet put } for pixels 0 number_pixels getinterval } bind def /GrayPseudoClassPacket { % % Get a PseudoClass packet; convert to grayscale. % % Parameters: % index: index into the colormap. % length: number of pixels minus one of this color (optional). % currentfile byte readhexstring pop 0 get /offset exch 3 mul def /color_packet colormap offset 3 getinterval def color_packet 0 get 0.299 mul color_packet 1 get 0.587 mul add color_packet 2 get 0.114 mul add cvi /gray_packet exch def compression 0 gt { /number_pixels 1 def } { currentfile byte readhexstring pop 0 get /number_pixels exch 1 add def } ifelse 0 1 number_pixels 1 sub { pixels exch gray_packet put } for pixels 0 number_pixels getinterval } bind def /PseudoClassPacket { % % Get a PseudoClass packet. % % Parameters: % index: index into the colormap. % length: number of pixels minus one of this color (optional). % currentfile byte readhexstring pop 0 get /offset exch 3 mul def /color_packet colormap offset 3 getinterval def compression 0 gt { /number_pixels 3 def } { currentfile byte readhexstring pop 0 get /number_pixels exch 1 add 3 mul def } ifelse 0 3 number_pixels 1 sub { pixels exch color_packet putinterval } for pixels 0 number_pixels getinterval } bind def /PseudoClassImage { % % Display a PseudoClass image. % % Parameters: % class: 0-PseudoClass or 1-Grayscale. % currentfile buffer readline pop token pop /class exch def pop class 0 gt { currentfile buffer readline pop token pop /depth exch def pop /grays columns 8 add depth sub depth mul 8 idiv string def columns rows depth [ columns 0 0 rows neg 0 rows ] { currentfile grays readhexstring pop } image } { % % Parameters: % colors: number of colors in the colormap. % colormap: red, green, blue color packets. % currentfile buffer readline pop token pop /colors exch def pop /colors colors 3 mul def /colormap colors string def currentfile colormap readhexstring pop pop systemdict /colorimage known { columns rows 8 [ columns 0 0 rows neg 0 rows ] { PseudoClassPacket } false 3 colorimage } { % % No colorimage operator; convert to grayscale. % columns rows 8 [ columns 0 0 rows neg 0 rows ] { GrayPseudoClassPacket } image } ifelse } ifelse } bind def /DisplayImage { % % Display a DirectClass or PseudoClass image. % % Parameters: % x & y translation. % x & y scale. % label pointsize. % image label. % image columns & rows. % class: 0-DirectClass or 1-PseudoClass. % compression: 0-RunlengthEncodedCompression or 1-NoCompression. % hex 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%%BeginDocument: fig5b.eps %!PS-Adobe-3.0 EPSF-3.0 %%Creator: (ImageMagick) %%Title: (fig5b.eps) %%CreationDate: (Thu Dec 19 11:22:00 2002) %%BoundingBox: 0 0 575 215 %%DocumentData: Clean7Bit %%LanguageLevel: 1 %%Pages: 0 %%EndComments %%BeginDefaults %%PageOrientation: Portrait %%EndDefaults %%BeginProlog % % Display a color image. The image is displayed in color on % Postscript viewers or printers that support color, otherwise % it is displayed as grayscale. % /buffer 512 string def /byte 1 string def /color_packet 3 string def /pixels 768 string def /DirectClassPacket { % % Get a DirectClass packet. % % Parameters: % red. % green. % blue. % length: number of pixels minus one of this color (optional). % currentfile color_packet readhexstring pop pop compression 0 gt { /number_pixels 3 def } { currentfile byte readhexstring pop 0 get /number_pixels exch 1 add 3 mul def } ifelse 0 3 number_pixels 1 sub { pixels exch color_packet putinterval } for pixels 0 number_pixels getinterval } bind def /DirectClassImage { % % Display a DirectClass image. % systemdict /colorimage known { columns rows 8 [ columns 0 0 rows neg 0 rows ] { DirectClassPacket } false 3 colorimage } { % % No colorimage operator; convert to grayscale. % columns rows 8 [ columns 0 0 rows neg 0 rows ] { GrayDirectClassPacket } image } ifelse } bind def /GrayDirectClassPacket { % % Get a DirectClass packet; convert to grayscale. % % Parameters: % red % green % blue % length: number of pixels minus one of this color (optional). % currentfile color_packet readhexstring pop pop color_packet 0 get 0.299 mul color_packet 1 get 0.587 mul add color_packet 2 get 0.114 mul add cvi /gray_packet exch def compression 0 gt { /number_pixels 1 def } { currentfile byte readhexstring pop 0 get /number_pixels exch 1 add def } ifelse 0 1 number_pixels 1 sub { pixels exch gray_packet put } for pixels 0 number_pixels getinterval } bind def /GrayPseudoClassPacket { % % Get a PseudoClass packet; convert to grayscale. % % Parameters: % index: index into the colormap. % length: number of pixels minus one of this color (optional). % currentfile byte readhexstring pop 0 get /offset exch 3 mul def /color_packet colormap offset 3 getinterval def color_packet 0 get 0.299 mul color_packet 1 get 0.587 mul add color_packet 2 get 0.114 mul add cvi /gray_packet exch def compression 0 gt { /number_pixels 1 def } { currentfile byte readhexstring pop 0 get /number_pixels exch 1 add def } ifelse 0 1 number_pixels 1 sub { pixels exch gray_packet put } for pixels 0 number_pixels getinterval } bind def /PseudoClassPacket { % % Get a PseudoClass packet. % % Parameters: % index: index into the colormap. % length: number of pixels minus one of this color (optional). % currentfile byte readhexstring pop 0 get /offset exch 3 mul def /color_packet colormap offset 3 getinterval def compression 0 gt { /number_pixels 3 def } { currentfile byte readhexstring pop 0 get /number_pixels exch 1 add 3 mul def } ifelse 0 3 number_pixels 1 sub { pixels exch color_packet putinterval } for pixels 0 number_pixels getinterval } bind def /PseudoClassImage { % % Display a PseudoClass image. % % Parameters: % class: 0-PseudoClass or 1-Grayscale. % currentfile buffer readline pop token pop /class exch def pop class 0 gt { currentfile buffer readline pop token pop /depth exch def pop /grays columns 8 add depth sub depth mul 8 idiv string def columns rows depth [ columns 0 0 rows neg 0 rows ] { currentfile grays readhexstring pop } image } { % % Parameters: % colors: number of colors in the colormap. % colormap: red, green, blue color packets. % currentfile buffer readline pop token pop /colors exch def pop /colors colors 3 mul def /colormap colors string def currentfile colormap readhexstring pop pop systemdict /colorimage known { columns rows 8 [ columns 0 0 rows neg 0 rows ] { PseudoClassPacket } false 3 colorimage } { % % No colorimage operator; convert to grayscale. % columns rows 8 [ columns 0 0 rows neg 0 rows ] { GrayPseudoClassPacket } image } ifelse } ifelse } bind def /DisplayImage { % % Display a DirectClass or PseudoClass image. % % Parameters: % x & y translation. % x & y scale. % label pointsize. % image label. % image columns & rows. % class: 0-DirectClass or 1-PseudoClass. % compression: 0-RunlengthEncodedCompression or 1-NoCompression. % hex 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0504001505020008050700000107000205ac000205ff054c00070507000c05080001050f 00010105000305ab000305ff055d0005052100050500000305ab000205ff056000020529 000205ac000205ff056100000529000305ab000205ff058d000205ab000205ff058d0002 05ab000205ff058e000305a9000205ff058e000405a7000305ff0590000305a6000205ff 0592000305a3000405ff05930003059f000605ff05950003059b000705ff059800030596 000905ff059b0004058f000c05ff059e00040589000e05ff05a200040581001105ff05a7 00050577001405ff05ae0006056a001805ff05b60006055d001c05ff05bf0008054b0022 05ff05c9000a0537002805ff05d600110510003a05ff05e4004b05ff05f8003605ff05ff 0512001005ff05ff05ff05ff05ff05ff05ff05ff05ff05ff051c %%EndData end %%PageTrailer %%Trailer %%BoundingBox: 0 0 575 215 %%EOF %%EndDocument @endspecial 18126 17014 a @beginspecial 0 @llx 0 @lly 575 @urx 215 @ury 1417 @rwi @setspecial %%BeginDocument: fig5c.eps %!PS-Adobe-3.0 EPSF-3.0 %%Creator: (ImageMagick) %%Title: (fig5c.eps) %%CreationDate: (Thu Dec 19 11:22:10 2002) %%BoundingBox: 0 0 575 215 %%DocumentData: Clean7Bit %%LanguageLevel: 1 %%Pages: 0 %%EndComments %%BeginDefaults %%PageOrientation: Portrait %%EndDefaults %%BeginProlog % % Display a color image. The image is displayed in color on % Postscript viewers or printers that support color, otherwise % it is displayed as grayscale. % /buffer 512 string def /byte 1 string def /color_packet 3 string def /pixels 768 string def /DirectClassPacket { % % Get a DirectClass packet. % % Parameters: % red. % green. % blue. % length: number of pixels minus one of this color (optional). % currentfile color_packet readhexstring pop pop compression 0 gt { /number_pixels 3 def } { currentfile byte readhexstring pop 0 get /number_pixels exch 1 add 3 mul def } ifelse 0 3 number_pixels 1 sub { pixels exch color_packet putinterval } for pixels 0 number_pixels getinterval } bind def /DirectClassImage { % % Display a DirectClass image. % systemdict /colorimage known { columns rows 8 [ columns 0 0 rows neg 0 rows ] { DirectClassPacket } false 3 colorimage } { % % No colorimage operator; convert to grayscale. % columns rows 8 [ columns 0 0 rows neg 0 rows ] { GrayDirectClassPacket } image } ifelse } bind def /GrayDirectClassPacket { % % Get a DirectClass packet; convert to grayscale. % % Parameters: % red % green % blue % length: number of pixels minus one of this color (optional). % currentfile color_packet readhexstring pop pop color_packet 0 get 0.299 mul color_packet 1 get 0.587 mul add color_packet 2 get 0.114 mul add cvi /gray_packet exch def compression 0 gt { /number_pixels 1 def } { currentfile byte readhexstring pop 0 get /number_pixels exch 1 add def } ifelse 0 1 number_pixels 1 sub { pixels exch gray_packet put } for pixels 0 number_pixels getinterval } bind def /GrayPseudoClassPacket { % % Get a PseudoClass packet; convert to grayscale. % % Parameters: % index: index into the colormap. % length: number of pixels minus one of this color (optional). % currentfile byte readhexstring pop 0 get /offset exch 3 mul def /color_packet colormap offset 3 getinterval def color_packet 0 get 0.299 mul color_packet 1 get 0.587 mul add color_packet 2 get 0.114 mul add cvi /gray_packet exch def compression 0 gt { /number_pixels 1 def } { currentfile byte readhexstring pop 0 get /number_pixels exch 1 add def } ifelse 0 1 number_pixels 1 sub { pixels exch gray_packet put } for pixels 0 number_pixels getinterval } bind def /PseudoClassPacket { % % Get a PseudoClass packet. % % Parameters: % index: index into the colormap. % length: number of pixels minus one of this color (optional). % currentfile byte readhexstring pop 0 get /offset exch 3 mul def /color_packet colormap offset 3 getinterval def compression 0 gt { /number_pixels 3 def } { currentfile byte readhexstring pop 0 get /number_pixels exch 1 add 3 mul def } ifelse 0 3 number_pixels 1 sub { pixels exch color_packet putinterval } for pixels 0 number_pixels getinterval } bind def /PseudoClassImage { % % Display a PseudoClass image. % % Parameters: % class: 0-PseudoClass or 1-Grayscale. % currentfile buffer readline pop token pop /class exch def pop class 0 gt { currentfile buffer readline pop token pop /depth exch def pop /grays columns 8 add depth sub depth mul 8 idiv string def columns rows depth [ columns 0 0 rows neg 0 rows ] { currentfile grays readhexstring pop } image } { % % Parameters: % colors: number of colors in the colormap. % colormap: red, green, blue color packets. % currentfile buffer readline pop token pop /colors exch def pop /colors colors 3 mul def /colormap colors string def currentfile colormap readhexstring pop pop systemdict /colorimage known { columns rows 8 [ columns 0 0 rows neg 0 rows ] { PseudoClassPacket } false 3 colorimage } { % % No colorimage operator; convert to grayscale. % columns rows 8 [ columns 0 0 rows neg 0 rows ] { GrayPseudoClassPacket } image } ifelse } ifelse } bind def /DisplayImage { % % Display a DirectClass or PseudoClass image. % % Parameters: % x & y translation. % x & y scale. % label pointsize. % image label. % image columns & rows. % class: 0-DirectClass or 1-PseudoClass. % compression: 0-RunlengthEncodedCompression or 1-NoCompression. % hex color packets. % gsave currentfile buffer readline pop token pop /x exch def token pop /y exch def pop x y translate currentfile buffer readline pop token pop /x exch def token pop /y exch def pop currentfile buffer readline pop token pop /pointsize exch def pop /Helvetica findfont pointsize scalefont setfont x y scale currentfile buffer readline pop token pop /columns exch def token pop /rows exch def pop currentfile buffer readline pop token pop /class exch def pop currentfile buffer readline pop token pop /compression exch def pop class 0 gt { PseudoClassImage } { DirectClassImage } ifelse grestore } bind def %%EndProlog %%Page: 1 1 %%PageBoundingBox: 0 0 575 215 userdict begin %%BeginData: DisplayImage 0 0 576 216 12 576 216 1 0 0 8 000000 00cc99 595959 59bfa5 d8d8d8 ffffff 010203 010203 05ff05ff05ff05ff05ff05ff05ff05ff05ff05ff05ff05ff05ff05ff05ff05ff05ff05ff 05ff05ff05ff05ff05ff05ff05ff05d0000a0508000405ff05ff0525000b0508000b0508 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b(is)g(called)h(the)f(adi-) 6075 58914 y(abatic)e(limit.)928 b(It)513 b(corresp)31 b(onds)512 b(to)j(a)e(forcing)i(with)g(frequency)e(whic)-31 b(h)515 b(is)e(m)-31 b(uc)g(h)514 b(smaller)6075 60242 y(than)563 b(the)f(time)i(scale)e(asso)31 b(ciated)564 b(with)f(the)g(\015o)-31 b(w)563 b(along)h(the)e(separatrix.)1073 b(The)562 b(tradi-)6075 61571 y(tional)386 b(w)-31 b(a)g(y)385 b(of)f(analyzing)i(this)e(limit)i(is)e(b)-31 b(y)384 b(using)g(the)g(adiabatic)i(appro)-31 b(ximation.)540 b(In)384 b(this)6075 62899 y(appro)-31 b(ximation)508 b(one)d(considers)g(solutions)h(to)f(the)g(frozen)g(Hamiltonian)k Fn(H)90 b Fs(\()p Fn(x;)184 b(y)40 b(;)184 b(\022)31 b Fs(;)184 b(0\))536 b(=)6075 64227 y Fn(H)6995 64393 y Fo(0)7491 64227 y Fs(\()p Fn(x;)184 b(y)40 b Fs(;)184 b(0\))324 b(+)d Fn(H)13528 64393 y Fo(1)14025 64227 y Fs(\()p Fn(x;)184 b(y)40 b(;)184 b(\022)31 b Fs(;)184 b(0\),)513 b(namely)483 b(the)f(time-dep)31 b(enden)-31 b(t)483 b(oscillations)i(are)c(no)-31 b(w)483 b(\014xed)6075 65556 y(at)408 b(the)f(frozen)h(phase)f Fn(\022)31 b Fs(.)606 b(One)407 b(then)h(studies)f(adiabatic)j(v)-61 b(ariables)408 b(\(to)g(leading)h(order,)417 b(the)6075 66884 y(action\),)330 b(and)318 b(asserts)e(that)j(in)f(the)f (nonlinear)i(case,)328 b(as)317 b(long)i(as)e(the)h(solutions)h(are)e (b)31 b(ounded)6075 68213 y(a)-31 b(w)g(a)g(y)438 b(from)f(the)f (separatrix,)455 b(suc)-31 b(h)436 b(v)-61 b(ariables)436 b(cannot)i(c)-31 b(hange)437 b(b)-31 b(y)437 b(m)-31 b(uc)g(h)437 b(due)f(to)h(the)f(p)31 b(er-)6075 69541 y(sistence)428 b(of)g(KAM)g(tori.)671 b(F)-92 b(urthermore,)442 b(when)428 b(the)h(solution)h(crosses)d(the)h(separatrix)h(one)p eop %%Page: 18 18 18 17 bop 6075 3345 a Fo(18)14390 b(VERED)299 b(R)-24 b(OM-KED)g(AR.)6075 6001 y Fs(can)440 b(estimate)j(the)d(resulting)i(c) -31 b(hange)441 b(in)g(the)f(adiabatic)j(in)-31 b(v)-61 b(ariances)442 b(and)e(the)h(phases)f(b)-31 b(y)6075 7330 y(constructing)300 b(an)f(adiabatic)j(separatrix)e(mapping)h 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b(a)h(p)31 b(ositiv)-31 b(e)406 b(constan)-31 b(t)405 b(and)g(the)6075 27377 y(higher)439 b(order)g(terms)g(are)f(small)j(for)p 22299 26768 V 439 w Fn(!)40 b Fs(\()p Fn(\027)70 b Fs(\))425 b Fn(<)439 b(!)26959 26976 y Fk(\003)27468 27377 y Fs(\()p Fn(T)154 b Fs(\).)702 b(Recall)440 b(that)h(in)e(the)g(limit)j Fn(\027)494 b Fl(!)424 b Fs(0)45190 26976 y Fo(+)6075 28706 y Fs(\(whic)-31 b(h,)370 b(b)-31 b(y)369 b(A3)g(corresp)31 b(onds)367 b(to)j(the)f(limit)p 25245 28096 V 370 w Fn(!)40 b Fs(\()p Fn(\027)70 b Fs(\))309 b Fl(!)e Fs(0)29727 28304 y Fo(+)30463 28706 y Fs(\),)369 b(there)f(are)h Fn(N)121 b Fs(\(0)38241 28304 y Fo(+)38977 28706 y Fs(\))368 b(top)31 b(ologically)6075 30034 y(transv)-31 b(erse)429 b(primary)g(homo)31 b(clinic)432 b(orbits,)445 b Fn(p)25370 29632 y Ff(n)26380 30034 y Fs(=)408 b Fn(p)28206 29632 y Ff(n)28808 30034 y Fs(\()p Fn(t)p Fs(;)184 b Fn(\034)30738 29632 y Ff(n)30613 30309 y Fo(0)31342 30034 y Fn(;)g(\027)70 b Fs(\))p Fn(;)184 b(n)411 b Fs(=)d(1)p Fn(;)184 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Ff(\022)41797 38979 y Fn(\026)p Fs(\()p Fn(R)9 b Fs(\()p Fn(\022)31 b Fs(\)\))p Fq(,)6075 40308 y(and)358 b Fn(N)121 b Fs(\(0)10180 39906 y Fo(+)10916 40308 y Fs(\))308 b Fl(\025)f Fs(2)p Fq(.)498 b(Then,)366 b(as)p 18783 39698 V 358 w Fn(!)39 b Fs(\()p Fn(\027)70 b Fs(\))309 b Fl(!)f Fs(0)23265 39906 y Fo(+)24000 40308 y Fq(,)366 b(the)358 b(primary)g(homo)-57 b(clinic)360 b(orbits)e Fn(p)39835 39906 y Ff(n)40437 40308 y Fs(\()p Fn(t)p Fs(;)184 b Fn(\034)42367 39906 y Ff(n)42242 40582 y Fo(0)42971 40308 y Fn(;)g(\027)70 b Fs(\))309 b Fl(!)6075 41636 y Fn(q)6569 41802 y Ff(h)7142 41636 y Fs(\()p Fn(t)p Fs(;)184 b Fn(\022)8983 41802 y Ff(n)9833 41636 y Fs(+)p 10940 41026 V 246 w Fn(!)40 b Fs(\()p Fn(\027)70 b Fs(\))p Fn(t)p Fs(\))397 b Fq(and:)19940 42992 y Fn(\026)p Fs(\()p Fn(R)9 b Fs(\()p Fn(\022)22837 43158 y Ff(n)23439 42992 y Fs(\)\))309 b(=)e Fn(\026)p Fs(\()p Fn(R)27723 42535 y Ff(n)27714 43266 y Fo(0)28325 42992 y Fs(\))247 b(+)f Fn(o)p Fs(\(1\))6075 44581 y Fq(wher)-57 b(e)396 b Fn(R)10051 44179 y Ff(n)10042 44856 y Fo(0)11048 44581 y Fq(denotes)g(the)g(r)-57 b(e)g(gion)397 b(enclose)-57 b(d)397 b(by)g Fn(U)121 b Fs([)p Fn(\015)61 b(;)184 b(p)28837 44179 y Ff(n)29441 44581 y Fs(])396 b Fq(and)g Fn(S)64 b Fs([)p Fn(\015)d(;)184 b(p)35026 44179 y Ff(n)35630 44581 y Fs(])p Fq(.)6075 46589 y(Pr)-57 b(o)g(of.)554 b Fs(See)486 b([10)r(],)516 b(where)486 b(it)h(is)f(pro)-31 b(v)g(ed)486 b(that)i(to)f(leading)g (order)f(the)g(adiabatic)j(Melnik)-31 b(o)g(v)6075 47918 y(function,)426 b(whic)-31 b(h)414 b(measures)f(the)g(distance)i(b)31 b(et)-31 b(w)g(een)414 b(the)f(stable)h(and)g(unstable)g(manifolds)6075 49246 y(is)369 b(giv)-31 b(en,)371 b(to)f(leading)h(order,)e(b)-31 b(y)20649 48810 y Ff(d)p 20426 48991 907 45 v 20426 49628 a(d\022)21465 49246 y Fn(\026)p Fs(\()p Fn(R)9 b Fs(\()p Fn(\022)31 b Fs(\)\))p Fn(:)19504 b Fd(\003)6075 51279 y Fg(Corollary)443 b(4.)553 b Fq(As)p 14971 50669 729 45 v 396 w Fn(!)39 b Fs(\()p Fn(\027)70 b Fs(\))309 b Fl(!)f Fs(0)p 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b(erimen)-26 b(ts)304 b(in)g(sto)26 b(c)-26 b(hasticit)g(y)305 b(and)f(homo)26 b(clinic)306 b(oscilla-)8009 28583 y(tions.)314 b Fp(annals.)340 b(NY)h(A)-49 b(c.)341 b(Sc.)p Fx(,)314 b(357:108{118,)319 b(1980.)6545 29690 y([3])472 b(R.)280 b(Easton.)g(T)-78 b(rellises)280 b(formed)f(b)-26 b(y)278 b(stable)i(and)f(unstable)h(manifolds)g(in)f(the)g(plane.)h Fp(T)-73 b(r)-49 b(ans.)308 b(A)-24 b(m.)308 b(Math.)8009 30797 y(So)-49 b(c.)p Fx(,)314 b(294:2,)j(1986.)6545 31904 y([4])472 b(Y.)403 b(Elsk)-26 b(ens)403 b(and)g(D.)g(Escande.)h (Slo)-26 b(wly)403 b(pulsating)h(separatrices)g(sw)-26 b(eep)403 b(homo)26 b(clinic)405 b(tangles)f(where)8009 33011 y(islands)378 b(m)-26 b(ust)377 b(b)26 b(e)377 b(small:)546 b(An)377 b(extension)g(of)g(classical)j(adiabatic)e (theory)-78 b(.)377 b Fp(Nonline)-49 b(arity)p Fx(,)393 b(4:615{667,)8009 34118 y(1991.)6545 35225 y([5])472 b(V.)330 b(Gelfreic)-26 b(h.)330 b(Melnik)-26 b(o)g(v)330 b(metho)26 b(d)330 b(and)g(exp)26 b(onen)-26 b(tially)331 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Fx(,)314 b(27:3{22,)j(1982.)6545 44081 y([9])472 b(T.)345 b(Kap)26 b(er)346 b(and)f(S.)g(Wiggins.)j(Lob) 26 b(e)345 b(area)h(in)f(adiabatic)i(systems.)f(In)f Fp(Nonline)-49 b(ar)371 b(Scienc)-49 b(e:)497 b(The)370 b(Next)8009 45188 y(De)-49 b(c)g(ade,)341 b(pr)-49 b(o)g(c.)340 b(CNLS)h(10th)e(A)-24 b(nnual)341 b(Conf.,)e(Physic)-49 b(a)339 b(D)p Fx(.)6075 46295 y([10])472 b(T.)460 b(J.)g(Kap)26 b(er)460 b(and)g(G.)h(Ko)-26 b(v)-52 b(a)-26 b(\024)-444 b(ci)-26 b(\024)-444 b(c.)461 b(A)e(geometric)j(criterion)e(for)g (adiabatic)i(c)-26 b(haos.)461 b Fp(J.)476 b(Math.)f(Phys.)p Fx(,)8009 47402 y(35\(3\):1202{1218,)320 b(1994.)6075 48509 y([11])472 b(R.)233 b(MacKa)-26 b(y)-78 b(,)249 b(J.)234 b(Meiss,)250 b(and)233 b(I.)g(P)-26 b(erciv)-52 b(al.)233 b(T)-78 b(ransp)26 b(ort)232 b(in)h(Hamiltonian)i(systems.)f Fp(Physic)-49 b(a)264 b(D)p Fx(,)233 b(13:55{81,)8009 49616 y(1984.)6075 50723 y([12])472 b(J.)f(Meiss.)g(Symplectic)g(maps,) 511 b(v)-52 b(ariational)472 b(principles,)511 b(and)470 b(transp)26 b(ort.)471 b Fp(R)-49 b(ev.)486 b(of)g(Mo)-49 b(dern)486 b(Phys.)p Fx(,)8009 51830 y(64\(3\):795{848,)319 b(1992.)6075 52936 y([13])472 b(J.)314 b(Meiss.)g(Av)-26 b(erage)314 b(exit)g(time)g(for)g(v)-26 b(olume)314 b(preserving)f (maps.)h Fp(Chaos)p Fx(,)g(7\(1\):139{147,)k(1997.)6075 54043 y([14])472 b(A.)423 b(Neish)-26 b(tadt.)423 b(The)f(separation)i (of)e(motions)i(in)f(systems)g(with)f(rapidly)g(rotating)i(phase.)f Fp(P.M.M.)8009 55150 y(USSR)p Fx(,)315 b(48:133{139,)j(1984.)6075 56257 y([15])472 b(A.)336 b(I.)f(Neish)-26 b(tadt.)337 b(P)-26 b(assage)337 b(through)e(a)h(separatrix)g(in)g(a)g(resonance)g (problem)g(with)g(a)g(slo)-26 b(wly-v)-52 b(arying)8009 57364 y(parameter.)314 b Fp(Prikl.)340 b(Mat.)f(Meh.)p Fx(,)314 b(39\(4-6\):1331{1334,)320 b(1975.)6075 58471 y([16])472 b(A.)385 b(I.)g(Ne)-105 b(\025)-366 b(\020sh)-26 b(tadt,)404 b(Cha)-105 b(\025)-366 b(\020k)-26 b(o)g(vski)-105 b(\025)-366 b(\020,)405 b(and)385 b(A.)g(A.)g(Chernik)-26 b(o)g(v.)383 b(Adiabatic)j(c)-26 b(haos)386 b(and)f(particle)g (di\013usion.)8009 59578 y Fp(Sov.)340 b(Phys.)f(JETP)p Fx(,)315 b(72\(3\):423{430,)k(1991.)6075 60685 y([17])472 b(H.)283 b(P)-26 b(oincar)g(\023)-444 b(e.)284 b Fp(L)-49 b(es)312 b(Metho)-49 b(ds)312 b(Nouvel)49 b(les)311 b(de)h(la)g(Me)-49 b(chanique)313 b(Celeste)p Fx(.)283 b(Gauthier-Villars,)291 b(P)-26 b(aris,)290 b(1892.)6075 61792 y([18])472 b(V.)349 b(Rom-Kedar)g(and)g(A.)g(C.)g(P)-26 b(o)52 b(je.)349 b(Univ)-26 b(ersal)349 b(prop)26 b(erties)349 b(of)g(c)-26 b(haotic)350 b(transp)26 b(ort)349 b(in)g(the)f(presence)h(of)8009 62899 y(di\013usion.)314 b Fp(Phys.)339 b(of)h(Fluids)p Fx(,)313 b(11\(8\):2044{2057,)319 b(1999.)6075 64006 y([19])472 b(V.)413 b(Rom-Kedar)h(and)g(S.)f(Wiggins.)j(T)-78 b(ransp)26 b(ort)412 b(in)i(t)-26 b(w)g(o-dimensional)414 b(maps.)h Fp(A)-24 b(r)-49 b(chive)433 b(for)f(R)-49 b(ational)8009 65113 y(Me)g(ch.)340 b(and)g(A)-24 b(nal.)p Fx(,)314 b(109\(3\):239{298,)320 b(1990.)6075 66220 y([20])472 b(C.)423 b(Soto-T)-78 b(revin~)-470 b(o)422 b(and)h(T.)g(J.)h(Kap)26 b(er.)423 b(Higher-order)g(melnik)-26 b(o)g(v)423 b(theory)g(for)g (adiabatic)i(systems.)e Fp(J.)8009 67327 y(Math.)339 b(Phys.)p Fx(,)313 b(37\(12\):6220{6249,)320 b(1996.)6075 68434 y([21])472 b(J.)399 b(L.)g(T)-78 b(enn)-26 b(yson,)419 b(J.)400 b(R.)f(Cary)-78 b(,)420 b(and)399 b(D.)g(F.)g(Escande.)h (Change)f(of)g(the)g(adiabatic)i(in)-26 b(v)-52 b(arian)-26 b(t)398 b(due)h(to)8009 69541 y(separatrix)314 b(crossing.)h Fp(Phys.)339 b(R)-49 b(ev.)340 b(L)-49 b(ett.)p Fx(,)313 b(56\(20\):2117{2120,)321 b(1986.)p eop %%Page: 20 20 20 19 bop 6075 3345 a Fo(20)14390 b(VERED)299 b(R)-24 b(OM-KED)g(AR.)6075 6001 y Fx([22])472 b(D.)303 b(T)-78 b(resc)-26 b(hev.)302 b(Width)g(of)g(sto)26 b(c)-26 b(hastic)304 b(la)-26 b(y)g(ers)303 b(in)g(near-in)-26 b(tegrable)303 b(t)-26 b(w)g(o-dimensional)303 b(symplectic)g(maps.)8009 7108 y Fp(Phys.)339 b(D)p Fx(,)314 b(116\(1-2\):21{43,)k(1998.)6075 8215 y([23])472 b(D.)300 b(T)-78 b(uraev.)298 b(P)-26 b(olynomial)301 b(appro)-26 b(ximations)301 b(of)e(symplectic)h (dynamics)g(and)f(ric)-26 b(hness)300 b(of)f(c)-26 b(haos)300 b(in)g(non-)8009 9322 y(h)-26 b(yp)26 b(erb)g(olic)314 b(area)g(preserving)g(maps.)g(submitted)g(preprin)-26 b(t,)313 b(2002.)7403 11398 y Fw(Dep)-59 b(ar)g(tment)336 b(of)f(computer)h(science)f(and)g(applied)f(ma)-59 b(thema)g(tics,)337 b(Weizmann)d(Institute.)7403 12505 y Fp(E-mail)340 b(addr)-49 b(ess)71 b Fx(:)418 b Fa(vered@wisdom.weizmann.ac.il)7403 13612 y Fp(URL)p Fx(:)314 b Fa (http://www.wisdom.weizmann.ac.il/~vered/)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF ---------------0301120609571--