Invariance principle and non-compact center foliations
Dynamical Systems
2023-12-07 v2
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.
Cite
@article{arxiv.2210.14989,
title = {Invariance principle and non-compact center foliations},
author = {Sylvain Crovisier and Mauricio Poletti},
journal= {arXiv preprint arXiv:2210.14989},
year = {2023}
}