On the ergodicity of partially hyperbolic systems

Amie Wilkinson; Keith Burns

On the ergodicity of partially hyperbolic systems

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arxiv math/0510234 v1 pith:SLNZWPMM submitted 2005-10-11 math.DS

Keith Burns , Amie Wilkinson This is my paper · ORCID

classification math.DS

keywords hyperbolicpartiallyergodicitysystemscenteraccessibilityassumptionbunching

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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 $C^{1+\gamma}$ partially hyperbolic systems.

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Decay of correlations for certain isometric extensions of Anosov flows
math.DS 2019-08 conditional novelty 7.0 of 10

Locally G-accessible isometric extensions of Anosov flows with C1 strong foliations and doubling conditional measures have exponential decay of correlations of all orders.

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