Regular and Chaotic Dynamics

, Volume 23, Issue 2, pp 161–177 | Cite as

Recent Results on the Dynamics of Higher-dimensional Hénon Maps

  • Stavros Anastassiou
  • Anastasios Bountis
  • Arnd Bäcker
Article
  • 13 Downloads

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 

Keywords

37D05 37D10 37D20 37D45 

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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  • Stavros Anastassiou
    • 1
  • Anastasios Bountis
    • 2
  • Arnd Bäcker
    • 3
    • 4
  1. 1.Center of Research and Applications of Nonlinear Systems (CRANS), University of PatrasDepartment of MathematicsRionGreece
  2. 2.Department of Mathematics, School of Science and TechnologyNazarbayev UniversityAstanaKazakhstan
  3. 3.Technische Universität DresdenInstitut für Theoretische Physik and Center for DynamicsDresdenGermany
  4. 4.Max-Planck-Institut für Physik komplexer SystemeDresdenGermany

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