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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