Non-transitive pseudo-Anosov flows
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866912902856835072 |
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| author | Barthelmé, Thomas Bonatti, Christian Mann, Kathryn |
| author_facet | Barthelmé, Thomas Bonatti, Christian Mann, Kathryn |
| contents | We study (topological) pseudo-Anosov flows from the perspective of the associated group actions on their orbit spaces and boundary at infinity. We extend the definition of Anosov-like action from [BFM22] from the transitive to the general non-transitive context and show that one can recover the basic sets of a flow, the Smale order on basic sets, and their essential features, from such general group actions. Using these tools, we prove that a pseudo-Anosov flow in a $3$ manifold is entirely determined by the associated action of the fundamental group on the boundary at infinity of its orbit space. We also give a proof that any topological pseudo-Anosov flow on an atoroidal 3-manifold is necessarily transitive, and prove that density of periodic orbits implies transitivity, in the topological rather than smooth case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_03586 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-transitive pseudo-Anosov flows Barthelmé, Thomas Bonatti, Christian Mann, Kathryn Dynamical Systems Geometric Topology We study (topological) pseudo-Anosov flows from the perspective of the associated group actions on their orbit spaces and boundary at infinity. We extend the definition of Anosov-like action from [BFM22] from the transitive to the general non-transitive context and show that one can recover the basic sets of a flow, the Smale order on basic sets, and their essential features, from such general group actions. Using these tools, we prove that a pseudo-Anosov flow in a $3$ manifold is entirely determined by the associated action of the fundamental group on the boundary at infinity of its orbit space. We also give a proof that any topological pseudo-Anosov flow on an atoroidal 3-manifold is necessarily transitive, and prove that density of periodic orbits implies transitivity, in the topological rather than smooth case. |
| title | Non-transitive pseudo-Anosov flows |
| topic | Dynamical Systems Geometric Topology |
| url | https://arxiv.org/abs/2411.03586 |