Accessibility and Ergodicity of Partially Hyperbolic Diffeomorphisms without Periodic Points
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866908300242583552 |
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| author | Feng, Ziqiang Ures, Raúl |
| author_facet | Feng, Ziqiang Ures, Raúl |
| contents | We prove that every $C^2$ conservative partially hyperbolic diffeomorphism of a closed 3-manifold without periodic points is ergodic, which gives an affirmative answer to the Ergodicity Conjecture by Hertz-Hertz-Ures in the absence of periodic points. We also show that a partially hyperbolic diffeomorphism of a closed 3-manifold $M$ with no periodic points is accessible if the non-wandering set is all of $M$ and the fundamental group $π_1(M)$ is not virtually solvable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_07062 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Accessibility and Ergodicity of Partially Hyperbolic Diffeomorphisms without Periodic Points Feng, Ziqiang Ures, Raúl Dynamical Systems 37A25, 37C25, 37C40, 37C86, 37D30, 57R30 We prove that every $C^2$ conservative partially hyperbolic diffeomorphism of a closed 3-manifold without periodic points is ergodic, which gives an affirmative answer to the Ergodicity Conjecture by Hertz-Hertz-Ures in the absence of periodic points. We also show that a partially hyperbolic diffeomorphism of a closed 3-manifold $M$ with no periodic points is accessible if the non-wandering set is all of $M$ and the fundamental group $π_1(M)$ is not virtually solvable. |
| title | Accessibility and Ergodicity of Partially Hyperbolic Diffeomorphisms without Periodic Points |
| topic | Dynamical Systems 37A25, 37C25, 37C40, 37C86, 37D30, 57R30 |
| url | https://arxiv.org/abs/2404.07062 |