On the ergodicity of partially hyperbolic systems

Details On the ergodicity of partially hyperbolic systems On the ergodicity of partially hyperbolic systems

2005-10-11

arxiv.org/abs/math/0510234v1

Mathematics

Dynamical Systems

46 pages, 4 figures

Scientific paper

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.

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