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This article is cited in 7 scientific papers (total 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.
Received: 11.01.2006 Accepted: 17.02.2006
Citation:
B.-S. Du, M.-C. Li, M. I. Malkin, “Topological horseshoes for Arneodo–Coullet–Tresser maps”, Regul. Chaotic Dyn., 11:2 (2006), 181–190
Linking options:
https://www.mathnet.ru/eng/rcd667 https://www.mathnet.ru/eng/rcd/v11/i2/p181
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