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Invariance principle and non-compact center foliations (2210.14989v2)

Published 26 Oct 2022 in math.DS

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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