Global smooth rigidity for toral automorphisms
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929427238092800 |
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| author | Kalinin, Boris Sadovskaya, Victoria Wang, Zhenqi |
| author_facet | Kalinin, Boris Sadovskaya, Victoria Wang, Zhenqi |
| contents | We study regularity of a conjugacy between a hyperbolic or partially hyperbolic toral automorphism $L$ and a $C^\infty$ diffeomorphism $f$ of the torus. For a very weakly irreducible hyperbolic automorphism $L$ we show that any $C^1$ conjugacy is $C^\infty$. For a very weakly irreducible ergodic partially hyperbolic automorphism $L$ we show that any $C^{1+\text{Hölder}}$ conjugacy is $C^\infty$. As a corollary, we improve regularity of the conjugacy to $C^\infty$ in prior local and global rigidity results. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_13877 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global smooth rigidity for toral automorphisms Kalinin, Boris Sadovskaya, Victoria Wang, Zhenqi Dynamical Systems 37D20, 37D30, 37C15 We study regularity of a conjugacy between a hyperbolic or partially hyperbolic toral automorphism $L$ and a $C^\infty$ diffeomorphism $f$ of the torus. For a very weakly irreducible hyperbolic automorphism $L$ we show that any $C^1$ conjugacy is $C^\infty$. For a very weakly irreducible ergodic partially hyperbolic automorphism $L$ we show that any $C^{1+\text{Hölder}}$ conjugacy is $C^\infty$. As a corollary, we improve regularity of the conjugacy to $C^\infty$ in prior local and global rigidity results. |
| title | Global smooth rigidity for toral automorphisms |
| topic | Dynamical Systems 37D20, 37D30, 37C15 |
| url | https://arxiv.org/abs/2407.13877 |