Measure rigidity for generalized u-Gibbs states and stationary measures via the factorization method
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arXiv
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| Format: | Preprint |
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2025
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| author | Brown, Aaron Eskin, Alex Filip, Simion Hertz, Federico Rodriguez |
| author_facet | Brown, Aaron Eskin, Alex Filip, Simion Hertz, Federico Rodriguez |
| contents | 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''. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_14042 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Measure rigidity for generalized u-Gibbs states and stationary measures via the factorization method Brown, Aaron Eskin, Alex Filip, Simion Hertz, Federico Rodriguez Dynamical Systems Classical Analysis and ODEs Geometric Topology 37C05, 37C40, 37H15, 37G05 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''. |
| title | Measure rigidity for generalized u-Gibbs states and stationary measures via the factorization method |
| topic | Dynamical Systems Classical Analysis and ODEs Geometric Topology 37C05, 37C40, 37H15, 37G05 |
| url | https://arxiv.org/abs/2502.14042 |