Koebe uniformization for infinitely connected attracting Fatou domains

Fuente: arXiv
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Main Authors: Wang, Xiaoguang, Zhong, Yi
Format: Preprint
Published: 2024
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_version_ 1866917699444015104
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