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Regul. Chaotic Dyn., 2018, Volume 23, Issue 2, Pages 161–177 (Mi rcd316)  

Recent Results on the Dynamics of Higher-dimensional Hénon Maps

Stavros Anastassioua, Anastasios Bountisb, Arnd Bäckercd

a Center of Research and Applications of Nonlinear Systems (CRANS), University of Patras, Department of Mathematics, GR-26500 Rion, Greece
b Department of Mathematics, School of Science and Technology, Nazarbayev University, Kabanbay-batyr 53, Astana, 010000 Kazakhstan
c Technische Universität Dresden, Institut für Theoretische Physik and Center for Dynamics, 01062 Dresden, Germany
d Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Strasse 38, 01187 Dresden, Germany

Abstract: We investigate different aspects of chaotic dynamics in Hénon maps of dimension higher than 2. First, we review recent results on the existence of homoclinic points in 2-d and 4-d such maps, by demonstrating how they can be located with great accuracy using the parametrization method. Then we turn our attention to perturbations of Hénon maps by an angle variable that are defined on the solid torus, and prove the existence of uniformly hyperbolic solenoid attractors for an open set of parameters.We thus argue that higher-dimensional Hénon maps exhibit a rich variety of chaotic behavior that deserves to be further studied in a systematic way.

Keywords: invariant manifolds, parametrization method, solenoid attractor, hyperbolic sets

Funding Agency
One of us (A. Bountis) gratefully acknowledges the hospitality of Alexey Borisov and Sergey Sokolov at Moscow Institute of Physics and Technology, as well as the support of the Social Policy grant of Nazarbayev University for his research and participation in the International Scientific Workshop “Recent Advances in Hamiltonian and Nonholonomic Dynamics”, Moscow, 14–18 June, 2017.


DOI: https://doi.org/10.1134/S156035471802003X

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Bibliographic databases:

Document Type: Article
MSC: 37D05, 37D10, 37D20, 37D45
Received: 14.11.2017
Accepted:27.01.2018
Language: English

Citation: Stavros Anastassiou, Anastasios Bountis, Arnd Bäcker, “Recent Results on the Dynamics of Higher-dimensional Hénon Maps”, Regul. Chaotic Dyn., 23:2 (2018), 161–177

Citation in format AMSBIB
\Bibitem{AnaBouBac18}
\by Stavros Anastassiou, Anastasios Bountis, Arnd B\"acker
\paper Recent Results on the Dynamics of Higher-dimensional Hénon Maps
\jour Regul. Chaotic Dyn.
\yr 2018
\vol 23
\issue 2
\pages 161--177
\mathnet{http://mi.mathnet.ru/rcd316}
\crossref{https://doi.org/10.1134/S156035471802003X}
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