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JOURNALS // Regular and Chaotic Dynamics // Archive

Regul. Chaotic Dyn., 2006 Volume 11, Issue 2, Pages 181–190 (Mi rcd667)

This article is cited in 7 papers

On the 70th birthday of L.P. Shilnikov

Topological horseshoes for Arneodo–Coullet–Tresser maps

B.-S. Dua, M.-C. Lib, M. I. Malkinc

a Institute of Mathematics, Academia Sinica, Taipei 115, Taiwan
b Department of Applied Mathematics, National Chiao Tung University, Hsinchu 300, Taiwan
c Department of Mathematics and Mechanics, Nizhny Novgorod State University, 603950 Nizhny Novgorod, Russia

Abstract: In this paper, we study the family of Arneodo–Coullet–Tresser maps $F (x, y, z) = (a x - b (y - z), b x + a (y - z), c x - d x k + e z)$ where $a, b, c, d, e$ are real parameters with $b d \neq 0$ 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.

Keywords: topological horseshoe, full shift, polynomial maps, generalized Hénon maps, nonwandering set, inverse limit, topological entropy.

MSC: 37C25, 37C70

Received: 11.01.2006
Accepted: 17.02.2006

Language: English

DOI: 10.1070/RD2006v011n02ABEH000344



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