We consider the set 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. This solves a conjecture of Pugh and Shub, in this setting.
Cite this article
Christian Bonatti, Marcelo Viana, Amie Wilkinson, Carlos Matheus, Abundance of stable ergodicity. Comment. Math. Helv. 79 (2004), no. 4, pp. 753–757DOI 10.1007/S00014-004-0819-8