Positive topological entropy for multidimensional perturbations of topologically crossing homoclinicity

Ming-Chia Li*, Ming Jiea Lyu

*Corresponding author for this work

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

In this paper, we consider a one-parameter family Fλ of continuous maps on ℝm or ℝm × ℝk with the singular map F0 having one of the forms (i) F0(x) = f(x), (ii) F0(x, y) = (f(x), g(x)), where g : ℝm → ℝk is continuous, and (iii) F 0(x, y) = (f(x), g(x, y)), where g : ℝm × ℝk → ℝk is continuous and locally trapping along the second variable y. We show that if f : ℝm → ℝm is a C1 diffeomorphism having a topologically crossing homoclinic point, then Fλ has positive topological entropy for all λ close enough to 0.

Original languageEnglish
Pages (from-to)243-252
Number of pages10
JournalDiscrete and Continuous Dynamical Systems
Volume30
Issue number1
DOIs
StatePublished - 1 May 2011

Keywords

  • Homoclinicity
  • Multidimensional perturbation
  • Topological crossing
  • Topological entropy

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