Piecewise quasiconformal dynamical systems of the unit circle
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913582668578816 |
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| author | Luo, Yusheng Ntalampekos, Dimitrios |
| author_facet | Luo, Yusheng Ntalampekos, Dimitrios |
| contents | We study piecewise quasiconformal covering maps of the unit circle. We provide sufficient conditions so that a conjugacy between two such dynamical systems has a quasiconformal or David extension to the unit disk. Our main result generalizes the main result of arXiv:2010.11256, which deals with piecewise analytic maps. As applications, we provide a classification of piecewise quasiconformal maps of the circle up to quasisymmetric conjugacy, we prove a general conformal mating theorem for Blaschke products, and we study the quasiconformal geometry of parabolic basins. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_14203 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Piecewise quasiconformal dynamical systems of the unit circle Luo, Yusheng Ntalampekos, Dimitrios Dynamical Systems Complex Variables Primary 30J10, 37F10, 37F31, Secondary 30C62, 30C65 We study piecewise quasiconformal covering maps of the unit circle. We provide sufficient conditions so that a conjugacy between two such dynamical systems has a quasiconformal or David extension to the unit disk. Our main result generalizes the main result of arXiv:2010.11256, which deals with piecewise analytic maps. As applications, we provide a classification of piecewise quasiconformal maps of the circle up to quasisymmetric conjugacy, we prove a general conformal mating theorem for Blaschke products, and we study the quasiconformal geometry of parabolic basins. |
| title | Piecewise quasiconformal dynamical systems of the unit circle |
| topic | Dynamical Systems Complex Variables Primary 30J10, 37F10, 37F31, Secondary 30C62, 30C65 |
| url | https://arxiv.org/abs/2411.14203 |