Geometric properties of partially hyperbolic measures and applications to measure rigidity
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Acceso en línea: | |
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| _version_ | 1866909377249673216 |
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| author | Eskin, Alex Potrie, Rafael Zhang, Zhiyuan |
| author_facet | Eskin, Alex Potrie, Rafael Zhang, Zhiyuan |
| contents | We give a geometric characterization of the quantitative non-integrability, introduced by Katz, of strong stable and unstable bundles of partially hyperbolic measures and sets in dimension 3. This is done via the use of higher order templates for the invariant bundles. Using the recent work of Katz, we derive some consequences, including the measure rigidity of $uu$-states and the existence of physical measures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_12981 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Geometric properties of partially hyperbolic measures and applications to measure rigidity Eskin, Alex Potrie, Rafael Zhang, Zhiyuan Dynamical Systems We give a geometric characterization of the quantitative non-integrability, introduced by Katz, of strong stable and unstable bundles of partially hyperbolic measures and sets in dimension 3. This is done via the use of higher order templates for the invariant bundles. Using the recent work of Katz, we derive some consequences, including the measure rigidity of $uu$-states and the existence of physical measures. |
| title | Geometric properties of partially hyperbolic measures and applications to measure rigidity |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2302.12981 |