Invariance of entropy for maps isotopic to Anosov
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866914656561397760 |
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| author | Carrasco, Pablo D. Lizana, Cristina Pujals, Enrique Vásquez, Carlos H. |
| author_facet | Carrasco, Pablo D. Lizana, Cristina Pujals, Enrique Vásquez, Carlos H. |
| contents | We prove the topological entropy remains constant inside the class of partially hyperbolic diffeomorphisms of $\mathbb{T}^d$ with simple central bundle (that is, when it decomposes into one dimensional sub-bundles with controlled geometry) and such that their induced action on $H_1(\mathbb{T}^d)$ is hyperbolic. In absence of the simplicity condition we construct a robustly transitive counter-example. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2001_05516 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Invariance of entropy for maps isotopic to Anosov Carrasco, Pablo D. Lizana, Cristina Pujals, Enrique Vásquez, Carlos H. Dynamical Systems 37A35, 37B40, 37D30 We prove the topological entropy remains constant inside the class of partially hyperbolic diffeomorphisms of $\mathbb{T}^d$ with simple central bundle (that is, when it decomposes into one dimensional sub-bundles with controlled geometry) and such that their induced action on $H_1(\mathbb{T}^d)$ is hyperbolic. In absence of the simplicity condition we construct a robustly transitive counter-example. |
| title | Invariance of entropy for maps isotopic to Anosov |
| topic | Dynamical Systems 37A35, 37B40, 37D30 |
| url | https://arxiv.org/abs/2001.05516 |