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arXiv · 2502.14042

Measure rigidity for generalized u-Gibbs states and stationary measures via the factorization method

Aaron Brown·Alex Eskin·Simion Filip·Federico Rodriguez Hertz
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Abstract

We obtain measure rigidity results for stationary measures of random walks generated by diffeomorphisms, and for actions of $\operatorname{SL}(2,\mathbb{R})$ 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 $1$-parameter flow and establishes extra invariance of a class of measures that we call ``generalized u-Gibbs states''.

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Aaron Brown, Alex Eskin, Simion Filip, Federico Rodriguez Hertz. 2025-02-19. Measure rigidity for generalized u-Gibbs states and stationary measures via the factorization method. https://arxiv.org/abs/2502.14042

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