Avila, Artur; Bochi, Jairo; Wilkinson, Amie
Nonuniform center bunching and the genericity of ergodicity among C 1 partially hyperbolic symplectomorphisms  [ Resserrement central non-uniforme et la généricité de l’ergodicité parmi les C 1 -symplectomorphismes partiellement hyperboliques ]
Annales scientifiques de l'École Normale Supérieure, Série 4 : Tome 42 (2009) no. 6 , p. 931-979
Zbl 1191.37017 | MR 2567746
doi : 10.24033/asens.2113
URL stable : http://www.numdam.org/item?id=ASENS_2009_4_42_6_931_0

Classification:  37D30,  37D25,  37J10
Mots clés: hyperbolicité partielle, resserrement central, ergodicité, difféomorphismes symplectiques
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.
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.

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