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On the ergodicity of partially hyperbolic systems

Keith Burns·Amie Wilkinson
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Abstract

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 $C^{1+γ}$ partially hyperbolic systems.

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Keith Burns, Amie Wilkinson. 2005-10-11. On the ergodicity of partially hyperbolic systems. https://arxiv.org/abs/math/0510234

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