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

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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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Authors and Affiliations

  1. IMERL-Facultad de Ingeniería, Universidad de la República, CC 30 Montevideo, Uruguay

    F. Rodriguez Hertz, M.A. Rodriguez Hertz & R. Ures

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  1. F. Rodriguez Hertz
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  2. M.A. Rodriguez Hertz
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  3. R. Ures
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Correspondence to F. Rodriguez Hertz.

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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

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