Abundance of stable ergodicity

  • Christian Bonatti

    Université de Bourgogne, Dijon, France
  • Marcelo Viana

    IMPA - Instituto Nacional de Matemática Pura e Aplicada, Rio de Janeiro, Brazil
  • Amie Wilkinson

    University of Chicago, USA
  • Carlos Matheus

    Université de Paris 13, Villetaneuse, France


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. 753–757

DOI 10.1007/S00014-004-0819-8