Accessibility and stable ergodicity for partially hyperbolic diffeomorphisms with 1d-center bundle

Details Accessibility and stable ergodicity for partially hyperbolic diffeomorphisms with 1d-center bundle Accessibility and stable ergodicity for partially hyperbolic diffeomorphisms with 1d-center bundle

2006-10-30

arxiv.org/abs/math/0610864v3

Mathematics

Dynamical Systems

22 pages, 9 figures

Scientific paper

We prove that stable ergodicity is C r open and dense among conservative partially hyperbolic diffeomorphisms with one-dimensional center bundle, for all r in [2,infty]. The proof follows Pugh-Shub program: among conservative partially hyperbolic diffeomorphisms with one-dimensional center bundle, accessibility is C r open and dense, and essential accessibility implies ergodicity.

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