Nonuniform center bunching and the genericity of ergodicity among C 1 partially hyperbolic symplectomorphisms

Artur Avila; Jairo Bochi; Amie Wilkinson

doi:10.24033/asens.2113

Nonuniform center bunching and the genericity of ergodicity among C ¹ partially hyperbolic symplectomorphisms

Artur Avila, Jairo Bochi, Amie Wilkinson

Mathematics

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

18 Scopus citations

Abstract

We introduce the notion of nonuniform center bunching for partially hyperbolic diffeomorphims, and extend previous results by Burns-Wilkinson and Avila-Santamaria-Viana. Combining this new technique with other constructions we prove that C¹ -generic partially hyperbolic symplectomorphisms are ergodic. We also construct new examples of stably ergodic partially hyperbolic diffeomorphisms.

Original language	English (US)
Pages (from-to)	931-979
Number of pages	49
Journal	Annales Scientifiques de l'Ecole Normale Superieure
Volume	42
Issue number	6
DOIs	https://doi.org/10.24033/asens.2113
State	Published - 2009

All Science Journal Classification (ASJC) codes

General Mathematics

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10.24033/asens.2113

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abstract = "We introduce the notion of nonuniform center bunching for partially hyperbolic diffeomorphims, and extend previous results by Burns-Wilkinson and Avila-Santamaria-Viana. Combining this new technique with other constructions we prove that C1 -generic partially hyperbolic symplectomorphisms are ergodic. We also construct new examples of stably ergodic partially hyperbolic diffeomorphisms.",

author = "Artur Avila and Jairo Bochi and Amie Wilkinson",

year = "2009",

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AU - Bochi, Jairo

AU - Wilkinson, Amie

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AB - We introduce the notion of nonuniform center bunching for partially hyperbolic diffeomorphims, and extend previous results by Burns-Wilkinson and Avila-Santamaria-Viana. Combining this new technique with other constructions we prove that C1 -generic partially hyperbolic symplectomorphisms are ergodic. We also construct new examples of stably ergodic partially hyperbolic diffeomorphisms.

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Nonuniform center bunching and the genericity of ergodicity among C ¹ partially hyperbolic symplectomorphisms

Abstract

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