A geometric criterion for positive topological entropy II: Homoclinic tangencies

Ale Jan Homburg, Howard Weiss

Research output: Contribution to journalReview article

8 Citations (Scopus)

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

Fingerprint

Homoclinic Point
Horseshoe
Topological Entropy
Homoclinic
Diffeomorphism
Homoclinic Tangency
Contact
entropy
Topological Conjugacy
shift
Periodic Points
Series

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

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A geometric criterion for positive topological entropy II : Homoclinic tangencies. / Homburg, Ale Jan; Weiss, Howard.

In: Communications In Mathematical Physics, Vol. 208, No. 2, 01.01.1999, p. 267-273.

Research output: Contribution to journalReview article

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