Transitive Anosov flows on non-compact manifolds
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908579974348800 |
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| author | Barthelmé, Thomas Lu, Lingfeng |
| author_facet | Barthelmé, Thomas Lu, Lingfeng |
| contents | In this article we study topological transitivity of Anosov flows on non-compact 3-manifolds. We provide homological conditions under which the lifts of a transitive Anosov flow to certain infinite covers of the manifold remain transitive. With some deep results in 3-manifold topology, we then deduce that such cover can be obtained for any non-graph manifold admitting a transitive Anosov flow. Moreover, for a large class of Anosov flows known as $\mathbb{R}$-covered, which are always transitive, we show that their lifts to any regular covers are either transitive or consist exclusively of wandering orbits. Finally, we construct a family of transitive Anosov flows on non-compact manifolds that satisfy a homotopical characterization of suspension flows, answering the flow version of a question concerning the existence of transitive Anosov diffeomorphisms on non-compact manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_22975 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Transitive Anosov flows on non-compact manifolds Barthelmé, Thomas Lu, Lingfeng Dynamical Systems Primary 37D20, 37D05, Secondary 37C27 In this article we study topological transitivity of Anosov flows on non-compact 3-manifolds. We provide homological conditions under which the lifts of a transitive Anosov flow to certain infinite covers of the manifold remain transitive. With some deep results in 3-manifold topology, we then deduce that such cover can be obtained for any non-graph manifold admitting a transitive Anosov flow. Moreover, for a large class of Anosov flows known as $\mathbb{R}$-covered, which are always transitive, we show that their lifts to any regular covers are either transitive or consist exclusively of wandering orbits. Finally, we construct a family of transitive Anosov flows on non-compact manifolds that satisfy a homotopical characterization of suspension flows, answering the flow version of a question concerning the existence of transitive Anosov diffeomorphisms on non-compact manifolds. |
| title | Transitive Anosov flows on non-compact manifolds |
| topic | Dynamical Systems Primary 37D20, 37D05, Secondary 37C27 |
| url | https://arxiv.org/abs/2503.22975 |