Abundance of stable ergodicity

Amie Wikinson | Bonatti, Christian | Matheus, Carlos | Viana, Marcelo

Keywords: stably ergodicity | partial hyperbolicity | volume preserving

We consider the set $\cP\cH_\omega(M)$ of volume preserving partially hyperbolic diffeomorphisms on a compact manifold having $1$-dimensional center bundle. We show that the volume measure is ergodic, and even Bernoulli, for any $C^2$ diffeomorphism in an open and dense subset of $\cP\cH_\omega(M)$. This solves a conjecture of Pugh and Shub, in this setting.

Anexos:

• stably.ps