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arXiv:math/0510234 [math.DS]AbstractReferencesReviewsResources

On the ergodicity of partially hyperbolic systems

Keith Burns, Amie Wilkinson

Published 2005-10-11Version 1

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 1-dimensional center bundle. We also obtain ergodicity results for $C^{1+\gamma}$ partially hyperbolic systems.

Comments: 46 pages, 4 figures
Categories: math.DS
Subjects: 37D30, 37C40
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