Commentarii Mathematici Helvetici


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Volume 92, Issue 3, 2017, pp. 467–512
DOI: 10.4171/CMH/417

Published online: 2017-07-27

Stable ergodicity and accessibility for certain partially hyperbolic diffeomorphisms with bidimensional center leaves

Vanderlei Horita[1] and Martin Sambarino

(1) Universidade Estadual Paulista, São José do Rio Preto, Brazil

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.

Keywords: Accessibility, ergodicity, stable ergodicity, partial hyperbolicity

Horita Vanderlei, Sambarino Martin: Stable ergodicity and accessibility for certain partially hyperbolic diffeomorphisms with bidimensional center leaves. Comment. Math. Helv. 92 (2017), 467-512. doi: 10.4171/CMH/417