Ergodic measures with large entropy have long unstable manifolds for $C^\infty$ surface diffeomorphisms
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866908443682537472 |
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| author | Luo, Chiyi Yang, Dawei |
| author_facet | Luo, Chiyi Yang, Dawei |
| contents | We prove that for ergodic measures with large entropy have long unstable manifolds for $C^\infty$ surface diffeomorphisms. Specifically, for any $α>0$, there exist constants $β>0$ and $c>0$ such that for every ergodic measure $μ$ with metric entropy large than $α$, the set of points with the size of unstable manifolds large than $β$ has $μ$-measure large than $c$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_07979 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Ergodic measures with large entropy have long unstable manifolds for $C^\infty$ surface diffeomorphisms Luo, Chiyi Yang, Dawei Dynamical Systems We prove that for ergodic measures with large entropy have long unstable manifolds for $C^\infty$ surface diffeomorphisms. Specifically, for any $α>0$, there exist constants $β>0$ and $c>0$ such that for every ergodic measure $μ$ with metric entropy large than $α$, the set of points with the size of unstable manifolds large than $β$ has $μ$-measure large than $c$. |
| title | Ergodic measures with large entropy have long unstable manifolds for $C^\infty$ surface diffeomorphisms |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2410.07979 |