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Invariance principle and non-compact center foliations

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arxiv 2210.14989 v2 pith:GLXJ2V7R submitted 2022-10-26 math.DS

Sylvain Crovisier , Mauricio Poletti This is my paper · ORCID
classification math.DS
keywords centeranosovflowsinvarianceinvariantmeasuremeasuresprinciple
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Partially hyperbolic diffeomorphisms homotopic to the identity in dimension three

    math.DS 2025-05 conditional novelty 8.0 of 10

    Conservative partially hyperbolic diffeomorphisms homotopic to the identity on closed 3-manifolds with non-virtually-solvable fundamental group are always accessible and hence ergodic.

  2. Margulis Measures on Expanding Foliations: Construction and Rigidity

    math.DS 2026-07 conditional novelty 6.0 of 10

    Under homogeneous exponential growth, every measure maximizing entropy along an expanding one-dimensional foliation has conditional measures equivalent to a canonically constructed weak Margulis measure.

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