- 99-25 Ale Jan Homburg and Howard Weiss
- A Geometric Criterion for Positive Topological Entropy
II: Homoclinic Tangencies
(449K, Postscript)
Jan 22, 99
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Abstract. In a series of important papers \cite{GS1, GS2} Gavrilov
and Shilnikov established a topological conjugacy between a
surface diffeomorphism having a dissipative hyperbolic
periodic point with certain types of {\it quadratic}
homoclinic tangencies and the full shift on two symbols,
thus exhibiting horseshoes near a tangential homoclinic
point. In this note, which should be viewed of as an addendum
to \cite{BW}, we extend this result by showing that such a
diffeomorphism with a homoclinic tangency having {\it any}
order contact, possible with {\it infinite} order contact,
possesses a horseshoe near the homoclinic point.
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