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arXiv · 1603.00053

Stable Ergodicity and Accessibility for certain Partially Hyperbolic Diffeomorphisms with Bidimensional Center Leaves

Vanderlei Horita·Martin Sambarino
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Abstract

We consider classes of partially hyperbolic diffeomorphism $f:M\to M$ with splitting $TM=E^s\oplus E^c\oplus E^u$ and $\dim E^c=2$. These classes include for instance (perturbations of) the product of Anosov and conservative surface diffeomorphisms, skew products of surface diffeomorphisms over Anosov, partially hyperbolic symplectomorphisms on manifolds of dimension four with bidimensional center foliation whose center leaves are all compact. We prove that accessibility holds in these classes for $C^1$ open and $C^r$ dense subsets and moreover they are stably ergodic.

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Vanderlei Horita, Martin Sambarino. 2016-02-29. Stable Ergodicity and Accessibility for certain Partially Hyperbolic Diffeomorphisms with Bidimensional Center Leaves. https://arxiv.org/abs/1603.00053

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