A geometric criterion for positive topological entropy II: Homoclinic tangencies

Ale Jan Homburg, Howard Weiss

Research output: Contribution to journalReview article

9 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)267-273
Number of pages7
JournalCommunications In Mathematical Physics
Volume208
Issue number2
DOIs
StatePublished - Jan 1 1999

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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