English

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 SL(2,R)\operatorname{SL}(2,\mathbb{R}) 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 11-parameter flow and establishes extra invariance of a class of measures that we call ``generalized u-Gibbs states''.

Keywords

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

R2 v1 2026-06-28T21:50:33.056Z