Recent Results on the Dynamics of Higher-dimensional Henon Maps

We investigate different aspects of chaotic dynamics in Henon 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 Henon 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 Henon maps exhibit a rich variety of chaotic behavior that deserves to be further studied in a systematic way.