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Artur Avila, Jairo Bochi, Amie Wilkinson
Nonuniform center bunching and the genericity of ergodicity among C^1 partially hyperbolic symplectomorphisms
Annales scientifiques de l'ENS 42, fascicule 6 (2009), 931-979

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Résumé :
Resserrement central non-uniforme et la généricité de l'ergodicité parmi les -symplectomorphismes partiellement hyperboliques
Nous introduisons une notion non-uniforme de resserrement central pour les difféomorphismes partiellement hyperboliques qui nous permet de généraliser quelques résultats de Burns–Wilkinson et Avila–Santamaria–Viana. Cette nouvelle technique est utilisée, en combinaison avec d'autres constructions, pour démontrer la généricité de l'ergodicité parmi les difféomorphismes symplectiques partiellement hyperboliques de classe C^1 . De plus, nous obtenons de nouveaux exemples de dynamiques stablement ergodiques.

Mots-clefs : Hyperbolicité partielle, resserrement central, ergodicité, difféomorphismes symplectiques

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 C^1 -generic partially hyperbolic symplectomorphisms are ergodic. We also construct new examples of stably ergodic partially hyperbolic diffeomorphisms.

Keywords: Partial hyperbolicity, center bunching, ergodicity, symplectic diffeomorphisms

Class. math. : 37D30, 37D25, 37J10

ISSN : 0012-9593
Publié avec le concours de : Centre National de la Recherche Scientifique

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