Pugh and Shub have conjectured that essential accessibility implies ergodicity, for a C^2, partially hyperbolic, volume-preserving diffeomorphism. We prove this conjecture under a mild center bunching assumption, which is satsified by all partially hyperbolic systems with one dimensional center bundle.
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The research in this article was supported by National Science Foundation grants DMS-0100416 and DMS-0408704. Needless to say, any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.
Authors' addresses: Keith Burns Department of Mathematics Northwestern University Evanston, IL 60208-2730 Amie Wilkinson Department of Mathematics Northwestern University Evanston, IL 60208-2730