Recent Results on the Dynamics of Higher-dimensional Hénon Maps

    2018, Volume 23, Number 2, pp.  161-177

    Author(s): Anastassiou  S., Bountis A., Bäcker A.

    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
    Citation: Anastassiou  S., Bountis A., Bäcker A., Recent Results on the Dynamics of Higher-dimensional Hénon Maps, Regular and Chaotic Dynamics, 2018, Volume 23, Number 2, pp. 161-177

    Access to the full text on the Springer website