Commentarii Mathematici Helvetici

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Volume 79, Issue 4, 2004, pp. 753–757
DOI: 10.1007/s00014-004-0819-8

Published online: 2004-12-31

Abundance of stable ergodicity

Christian Bonatti[1], Carlos Matheus[2], Marcelo Viana[3] and Amie Wilkinson[4]

(1) Université de Bourgogne, Dijon, France
(2) Université de Paris 13, Villetaneuse, France
(3) IMPA - Instituto Nacional de Matemática Pura e Aplicada, Rio de Janeiro, Brazil
(4) University of Chicago, USA

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.

Keywords: partial hyperbolicity, stable ergodicity, accessibility, Lyapunov exponents, nonuniform hyperbolicity

Bonatti Christian, Matheus Carlos, Viana Marcelo, Wilkinson Amie: Abundance of stable ergodicity. Comment. Math. Helv. 79 (2004), 753-757. doi: 10.1007/s00014-004-0819-8