Transitive partially hyperbolic diffeomorphisms in dimension three
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908740372922368 |
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| author | Feng, Ziqiang |
| author_facet | Feng, Ziqiang |
| contents | We prove that any $C^{1+α}$ transitive conservative partially hyperbolic diffeomorphism of a closed 3-manifold with virtually solvable fundamental group is ergodic. Consequently, in light of \cite{FP-classify}, this establishes the equivalence between transitivity and ergodicity for $C^{1+α}$ conservative partially hyperbolic diffeomorphisms in \emph{any} closed 3-manifold. Moreover, we provide a characterization of compact accessibility classes under transitivity, thereby giving a precise classification of all accessibility classes for transitive 3-dimensional partially hyperbolic diffeomorphisms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_24151 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Transitive partially hyperbolic diffeomorphisms in dimension three Feng, Ziqiang Dynamical Systems We prove that any $C^{1+α}$ transitive conservative partially hyperbolic diffeomorphism of a closed 3-manifold with virtually solvable fundamental group is ergodic. Consequently, in light of \cite{FP-classify}, this establishes the equivalence between transitivity and ergodicity for $C^{1+α}$ conservative partially hyperbolic diffeomorphisms in \emph{any} closed 3-manifold. Moreover, we provide a characterization of compact accessibility classes under transitivity, thereby giving a precise classification of all accessibility classes for transitive 3-dimensional partially hyperbolic diffeomorphisms. |
| title | Transitive partially hyperbolic diffeomorphisms in dimension three |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2512.24151 |