Abundance of stable ergodicity
Abundance of stable ergodicity
We consider the set \mathcal{PH}_\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 \mathcal{PH}_\omega(M) . This solves a conjecture of Pugh and …