On uniformly quasiconformal Anosov diffeomorphisms with two dimensional distributions
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866912151050911744 |
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| author | Zhang, Jiesong |
| author_facet | Zhang, Jiesong |
| contents | We prove that a transitive uniformly $u$-quasiconformal Anosov diffeomorphism with a two-dimensional unstable distribution has a globally defined stable holonomy. As a corollary, we are able to remove an additional assumption in a theorem of Kalinin-Sadovskaya, and deduce that all transitive uniformly quasiconformal Anosov diffeomorphisms are $C^{\infty}$-conjugate to affine Anosov diffeomorphisms on infra-torus. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_00251 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On uniformly quasiconformal Anosov diffeomorphisms with two dimensional distributions Zhang, Jiesong Dynamical Systems We prove that a transitive uniformly $u$-quasiconformal Anosov diffeomorphism with a two-dimensional unstable distribution has a globally defined stable holonomy. As a corollary, we are able to remove an additional assumption in a theorem of Kalinin-Sadovskaya, and deduce that all transitive uniformly quasiconformal Anosov diffeomorphisms are $C^{\infty}$-conjugate to affine Anosov diffeomorphisms on infra-torus. |
| title | On uniformly quasiconformal Anosov diffeomorphisms with two dimensional distributions |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2311.00251 |