(1) Laboratoire de Topologie, UMR 5584 du CNRS, Université de Bourgogne, BP 47 870, 21078 Cedex Dijon, France;(2) IMPA, Estrada D. Castorina 110, 22460-320 Rio de Janeiro, Brazil;(3) IMPA, Estrada D. Castorina 110, 22460-320 Rio de Janeiro, Brazil;(4) Department of Mathematics, Northwestern University, 2033 Sheridan Road, IL 60208-2730 Evanston, USA
Abstract:
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 C2 diffeomorphism in an open and dense subset of This solves a conjecture of Pugh and Shub, in this setting.
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 
This solves a conjecture of Pugh and Shub, in this setting.