JournalscmhVol. 92, No. 3pp. 467–512

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

  • Vanderlei Horita

    Universidade Estadual Paulista, São José do Rio Preto, Brazil
  • Martin Sambarino

    Universidad de la República, Montevideo, Uruguay
Stable ergodicity and accessibility for certain partially hyperbolic diffeomorphisms with bidimensional center leaves cover
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Abstract

We consider classes of partially hyperbolic diffeomorphism f:MMf:M\to M with splitting TM=EsEcEuTM=E^s\oplus E^c\oplus E^u and dimEc=2\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 C1C^1 open and CrC^r dense subsets and moreover they are stably ergodic.

Cite this article

Vanderlei Horita, Martin Sambarino, Stable ergodicity and accessibility for certain partially hyperbolic diffeomorphisms with bidimensional center leaves. Comment. Math. Helv. 92 (2017), no. 3, pp. 467–512

DOI 10.4171/CMH/417