Measure rigidity for generalized u-Gibbs states and stationary measures via the factorization method
Dynamical Systems
2025-02-21 v1 Classical Analysis and ODEs
Geometric Topology
Abstract
We obtain measure rigidity results for stationary measures of random walks generated by diffeomorphisms, and for actions of on smooth manifolds. Our main technical result, from which the rest of the theorems are derived, applies also to the case of a single diffeomorphism or -parameter flow and establishes extra invariance of a class of measures that we call ``generalized u-Gibbs states''.
Cite
@article{arxiv.2502.14042,
title = {Measure rigidity for generalized u-Gibbs states and stationary measures via the factorization method},
author = {Aaron Brown and Alex Eskin and Simion Filip and Federico Rodriguez Hertz},
journal= {arXiv preprint arXiv:2502.14042},
year = {2025}
}
Comments
278 pages, 4 figures