Koebe uniformization for infinitely connected attracting Fatou domains
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917699444015104 |
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| author | Wang, Xiaoguang Zhong, Yi |
| author_facet | Wang, Xiaoguang Zhong, Yi |
| contents | This paper works on the structure of infinitely connected Fatou damains of rational maps in terms of Koebe uniformization. Due to the complicated boundary behavior, the existing uniformization results are failed to apply in general. We proved that if the rational map is geometrically finite, then its infinitely connected attracting Fatou damain is conformally homeomorphic to a circle domain. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_13524 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Koebe uniformization for infinitely connected attracting Fatou domains Wang, Xiaoguang Zhong, Yi Complex Variables Dynamical Systems 30C20(Primary), 30C35(Secondary) This paper works on the structure of infinitely connected Fatou damains of rational maps in terms of Koebe uniformization. Due to the complicated boundary behavior, the existing uniformization results are failed to apply in general. We proved that if the rational map is geometrically finite, then its infinitely connected attracting Fatou damain is conformally homeomorphic to a circle domain. |
| title | Koebe uniformization for infinitely connected attracting Fatou domains |
| topic | Complex Variables Dynamical Systems 30C20(Primary), 30C35(Secondary) |
| url | https://arxiv.org/abs/2406.13524 |