Koebe uniformization for infinitely connected attracting Fatou domains
Complex Variables
2024-06-21 v1 Dynamical Systems
Abstract
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.
Cite
@article{arxiv.2406.13524,
title = {Koebe uniformization for infinitely connected attracting Fatou domains},
author = {Xiaoguang Wang and Yi Zhong},
journal= {arXiv preprint arXiv:2406.13524},
year = {2024}
}
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13 pages