Stavros Anastassiou

Patras, Greece


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, vol. 23, no. 2, pp. 161-177
Anastassiou  S.
We study vector fields of the plane preserving the Liouville form. We present their local models up to the natural equivalence relation and describe local bifurcations of low codimension. To achieve that, a classification of univariate functions is given according to a relation stricter than contact equivalence. In addition, we discuss their relation with strictly contact vector fields in dimension three. Analogous results for diffeomorphisms are also given.
Keywords: systems preserving the Liouville form, strictly contact systems, classification, bifurcations
Citation: Anastassiou  S.,  Dynamical Systems on the Liouville Plane and the Related Strictly Contact Systems, Regular and Chaotic Dynamics, 2016, vol. 21, nos. 7-8, pp. 862-873

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