Topological horseshoes for Arneodo - Coullet - Tresser maps

B. S. Du*, Ming-Chia Li, M. I. Malkin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

In this paper, we study the family of Arneodo-Coullet-Tresser maps F(x,y,z) = (ax - b(y - z), bx + a(y - z), cx - - dxk + ez) where a, b, c, d, e are real parameters with bd ≠ 0 and k > 1 is an integer. We find regions of parameters near anti-integrable limits and near singularities for which there exist hyperbolic invariant sets such that the restriction of F to these sets is conjugate to the full shift on two or three symbols.

Original languageEnglish
Pages (from-to)181-190
Number of pages10
JournalRegular and Chaotic Dynamics
Volume11
Issue number2
DOIs
StatePublished - 7 Jul 2006

Keywords

  • Full shift
  • Generalized Hénon maps
  • Inverse limit
  • Nonwandering set
  • Polynomial maps
  • Topological entropy
  • Topological horseshoe

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