A volume preserving nonuniformly hyperbolic diffeomorphism with arbitrary number of ergodic components and close to the identity
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866911019815665664 |
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| author | Chen, Jianyu Hu, Huyi Yang, Yun |
| author_facet | Chen, Jianyu Hu, Huyi Yang, Yun |
| contents | We prove that for any $\ell\in\NN\cup\{\infty\}$ and any $r\in \NN$, every compact smooth Riemannian manifold $\cM$ of $\dim \cM\ge 5$ carries a $C^\infty$ volume preserving nonuniformly hyperbolic diffeomorphism, which has exactly $\ell$ ergodic components (in fact, Bernoulli components) and is $C^r$ close to the identity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_00297 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A volume preserving nonuniformly hyperbolic diffeomorphism with arbitrary number of ergodic components and close to the identity Chen, Jianyu Hu, Huyi Yang, Yun Dynamical Systems 37C05, 37C10, 37C40, 37D25 We prove that for any $\ell\in\NN\cup\{\infty\}$ and any $r\in \NN$, every compact smooth Riemannian manifold $\cM$ of $\dim \cM\ge 5$ carries a $C^\infty$ volume preserving nonuniformly hyperbolic diffeomorphism, which has exactly $\ell$ ergodic components (in fact, Bernoulli components) and is $C^r$ close to the identity. |
| title | A volume preserving nonuniformly hyperbolic diffeomorphism with arbitrary number of ergodic components and close to the identity |
| topic | Dynamical Systems 37C05, 37C10, 37C40, 37D25 |
| url | https://arxiv.org/abs/2308.00297 |