Horizontality of partially hyperbolic foliations
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916649508012032 |
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| author | Hammerlindl, Andy Potrie, Rafael |
| author_facet | Hammerlindl, Andy Potrie, Rafael |
| contents | We show exactly which Seifert manifolds support partially hyperbolic dynamical systems. In particular, a circle bundle over a higher-genus surface supports a partially hyperbolic system if and only if it supports an Anosov flow. We also show for these systems that the center-stable and center-unstable foliations can be isotoped so that their leaves are transverse to the circle fibering. As a consequence, every partially hyperbolic system defined on the unit tangent bundle of a higher-genus surface is a collapsed Anosov flow. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_08077 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Horizontality of partially hyperbolic foliations Hammerlindl, Andy Potrie, Rafael Dynamical Systems 37D30, 37C86, 57R30 We show exactly which Seifert manifolds support partially hyperbolic dynamical systems. In particular, a circle bundle over a higher-genus surface supports a partially hyperbolic system if and only if it supports an Anosov flow. We also show for these systems that the center-stable and center-unstable foliations can be isotoped so that their leaves are transverse to the circle fibering. As a consequence, every partially hyperbolic system defined on the unit tangent bundle of a higher-genus surface is a collapsed Anosov flow. |
| title | Horizontality of partially hyperbolic foliations |
| topic | Dynamical Systems 37D30, 37C86, 57R30 |
| url | https://arxiv.org/abs/2503.08077 |