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

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. © 2009 Société Mathématique de France.