English

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.

Keywords

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}
}

Comments

13 pages

R2 v1 2026-06-28T17:12:10.376Z