Partially hyperbolic diffeomorphisms with one-dimensional neutral center on 3-manifolds
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2017
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| _version_ | 1866929355424268288 |
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| author | Zhang, Jinhua |
| author_facet | Zhang, Jinhua |
| contents | We prove that for any partially hyperbolic diffeomorphism with one dimensional neutral center on a 3-manifold, the center stable and center unstable foliations are complete; moreover, each leaf of center stable and center unstable foliations is a cylinder, a M$\ddot{o}$bius band or a plane.
Further properties of the Bonatti-Parwani-Potrie type of partially hyperbolic diffeomorphisms are studied. Such examples are obtained by composing the time $m$-map (for $m>0$ large) of a non-transitive Anosov flow $ϕ_t$ on an orientable 3-manifold with Dehn twists along some transverse tori, and the examples are partially hyperbolic with one-dimensional neutral center. We prove that the center foliation gives a topologically Anosov flow which is topologically equivalent to $ϕ_t$. We also prove that for the precise example constructed by Bonatti-Parwani-Potrie, the center stable and center unstable foliations are robustly complete. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1701_06176 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Partially hyperbolic diffeomorphisms with one-dimensional neutral center on 3-manifolds Zhang, Jinhua Dynamical Systems 37D30, 37C05, 37C5, 57R30 We prove that for any partially hyperbolic diffeomorphism with one dimensional neutral center on a 3-manifold, the center stable and center unstable foliations are complete; moreover, each leaf of center stable and center unstable foliations is a cylinder, a M$\ddot{o}$bius band or a plane. Further properties of the Bonatti-Parwani-Potrie type of partially hyperbolic diffeomorphisms are studied. Such examples are obtained by composing the time $m$-map (for $m>0$ large) of a non-transitive Anosov flow $ϕ_t$ on an orientable 3-manifold with Dehn twists along some transverse tori, and the examples are partially hyperbolic with one-dimensional neutral center. We prove that the center foliation gives a topologically Anosov flow which is topologically equivalent to $ϕ_t$. We also prove that for the precise example constructed by Bonatti-Parwani-Potrie, the center stable and center unstable foliations are robustly complete. |
| title | Partially hyperbolic diffeomorphisms with one-dimensional neutral center on 3-manifolds |
| topic | Dynamical Systems 37D30, 37C05, 37C5, 57R30 |
| url | https://arxiv.org/abs/1701.06176 |