On the ergodicity of partially hyperbolic systems
Keith Burns, Amie Wilkinson
Abstract
Pugh and Shub have conjectured that essential accessibility implies ergodicity, for a C2, 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 C1+γ partially hyperbolic systems.
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