Abstract:
In a series of important papers [GS1,GS2] Gavrilov and Shilnikov established a topological conjugacy between a surface diffeomorphism having a dissipative hyperbolic periodic point with certain types of 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 [BW] we extend this result by showing that such a diffeomorphism with a one-sided isolated homoclinic tangency having any order contact, possible with infinite order contact, possesses a horseshoe near the homoclinic point.
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Received: 2 March 1999 / Accepted: 14 May 1999
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Homburg, A., Weiss, H. A Geometric Criterion for Positive Topological Entropy¶II: Homoclinic Tangencies. Comm Math Phys 208, 267–273 (1999). https://doi.org/10.1007/s002200050757
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DOI: https://doi.org/10.1007/s002200050757