Partially hyperbolic diffeomorphisms homotopic to the identity in dimension three
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916770485370880 |
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| author | Feng, Ziqiang Ures, Raúl |
| author_facet | Feng, Ziqiang Ures, Raúl |
| contents | We show that any conservative partially hyperbolic diffeomorphism homotopic to the identity is accessible unless the fundamental group of its ambient 3-manifold is virtually solvable. As a consequence, such diffeomorphisms are ergodic, giving an affirmative answer to the Hertz-Hertz-Ures Ergodicity Conjecture in the homotopy class of identity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_00405 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Partially hyperbolic diffeomorphisms homotopic to the identity in dimension three Feng, Ziqiang Ures, Raúl Dynamical Systems 37A25, 37C86, 37D30, 57R30 We show that any conservative partially hyperbolic diffeomorphism homotopic to the identity is accessible unless the fundamental group of its ambient 3-manifold is virtually solvable. As a consequence, such diffeomorphisms are ergodic, giving an affirmative answer to the Hertz-Hertz-Ures Ergodicity Conjecture in the homotopy class of identity. |
| title | Partially hyperbolic diffeomorphisms homotopic to the identity in dimension three |
| topic | Dynamical Systems 37A25, 37C86, 37D30, 57R30 |
| url | https://arxiv.org/abs/2506.00405 |