Invariance principle and non-compact center foliations

Sylvain Crovisier; Mauricio Poletti

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arXiv · 2210.14989

Invariance principle and non-compact center foliations

Sylvain Crovisier·Mauricio Poletti

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Abstract

We prove a generalization of a so called "invariance principle" for partially hyperbolic diffeomorphisms: if an invariant probability measure has all its center Lyapunov exponents equal to zero then the measure admits a center disintegration that is invariant by stable and unstable holonomies. This was known for systems admitting a foliation by compact center leaves, and we extend it to a larger class which contains discretized Anosov flows. We use our result to classify measures of maximal entropy and study physical measures for perturbations of the time-one map of Anosov flows.

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Sylvain Crovisier, Mauricio Poletti. 2022-10-26. Invariance principle and non-compact center foliations. https://arxiv.org/abs/2210.14989

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