Topological horseshoes for Arneodo - Coullet - Tresser maps

B. S. Du; Ming-Chia Li; M. I. Malkin

doi:10.1111/j.1365-2052.2006.01427.x

Topological horseshoes for Arneodo - Coullet - Tresser maps

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

^*Corresponding author for this work

National Chiao Tung University

Research output: Contribution to journal › Article › peer-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 - - dx^k + 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 language	English
Pages (from-to)	181-190
Number of pages	10
Journal	Regular and Chaotic Dynamics
Volume	11
Issue number	2
DOIs	https://doi.org/10.1111/j.1365-2052.2006.01427.x
State	Published - 7 Jul 2006

Keywords

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

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title = "Topological horseshoes for Arneodo - Coullet - Tresser maps",

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.",

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year = "2006",

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AU - Du, B. S.

AU - Li, Ming-Chia

AU - Malkin, M. I.

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AB - 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.

KW - Full shift

KW - Generalized Hénon maps

KW - Inverse limit

KW - Nonwandering set

KW - Polynomial maps

KW - Topological entropy

KW - Topological horseshoe

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DO - 10.1111/j.1365-2052.2006.01427.x

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