 99139 J. C. Tatjer
 Three dimensional dissipative diffeomorphisms with homoclinic tangencies
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May 4, 99

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Abstract. Given a twoparameter family of threedimensional diffeomorphism
$\{ f_{a,b}\}_{a,b},$
with a dissipative (but not sectionally dissipative) saddle fixed point,
we prove that the existence
of a certain type of homoclinic tangency of the invariant manifolds,
implies that there exists a return map $f^n_{a,b},$ near the homoclinic orbit,
for values of the parameter near such tangency and for $n$ greater
enough, such that after
a change of variables and reparametrization depending on $n,$ this return
map tends to a simple quadratic map. This implies the existence of strange
attractors and infinitely many sinks as in other known cases. Moreover, there
appear attracting invariant circles, implying the existence of quasiperiodic
behaviour near the homoclinic tangency.
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