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

F. Rodriguez Hertz; M. A. Rodriguez Hertz; R. Ures

doi:10.1007/s00222-007-0100-z

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

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

Research output: Contribution to journal › Article › peer-review

88 Scopus citations

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.

Original language	English (US)
Pages (from-to)	353-381
Number of pages	29
Journal	Inventiones Mathematicae
Volume	172
Issue number	2
DOIs	https://doi.org/10.1007/s00222-007-0100-z
State	Published - May 2008

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1007/s00222-007-0100-z

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title = "Accessibility and stable ergodicity for partially hyperbolic diffeomorphisms with 1D-center bundle",

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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T1 - Accessibility and stable ergodicity for partially hyperbolic diffeomorphisms with 1D-center bundle

AU - Rodriguez Hertz, F.

AU - Rodriguez Hertz, M. A.

AU - Ures, R.

PY - 2008/5

Y1 - 2008/5

N2 - 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.

AB - 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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UR - https://www.scopus.com/pages/publications/41449086095#tab=citedBy

U2 - 10.1007/s00222-007-0100-z

DO - 10.1007/s00222-007-0100-z

M3 - Article

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JO - Inventiones Mathematicae

JF - Inventiones Mathematicae

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

Abstract

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