Nonuniform center bunching and the genericity of ergodicity among partially hyperbolic symplectomorphisms
Artur Avila, Jairo Bochi, Amie Wilkinson (2009)
Annales scientifiques de l'École Normale Supérieure
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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 -generic partially hyperbolic symplectomorphisms are ergodic. We also construct new examples of stably ergodic partially hyperbolic diffeomorphisms.