Abstract
We prove that stable ergodicity is C r open and dense among conservative partially hyperbolic diffeomorphisms with one-dimensional center bundle, for all r∈[2,∞].
The proof follows the Pugh–Shub program [29]: 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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Mathematics Subject Classification (2000)
Primary: 37D30, Secondary: 37A25
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Rodriguez Hertz, F., Rodriguez Hertz, M. & Ures, R. Accessibility and stable ergodicity for partially hyperbolic diffeomorphisms with 1D-center bundle . Invent. math. 172, 353–381 (2008). https://doi.org/10.1007/s00222-007-0100-z
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DOI: https://doi.org/10.1007/s00222-007-0100-z