亚纯函数的有界Fatou与Julia分支
动力系统
2024-12-10 v2 复变函数
摘要
我们完全刻画了作为亚纯函数的Fatou集与Julia集分支出现的的有界集。一方面，我们证明一个有界域是某个亚纯函数的Fatou分支当且仅当它是正则的。另一方面，我们证明一个平面连续统是某个亚纯函数的Julia分支当且仅当它具有空内部。我们通过用逼近论构造带游荡连续统的亚纯函数来实现这一点。
引用
@article{arxiv.2204.11781,
title = {Bounded Fatou and Julia components of meromorphic functions},
author = {David Martí-Pete and Lasse Rempe and James Waterman},
journal= {arXiv preprint arXiv:2204.11781},
year = {2024}
}
备注
15 pages, 4 figures. V2: We have revised the introduction, and introduced two new sections: Section 2 discusses and compare topological properties of Fatou components, while Section 3 establishes that certain bounded regular domains cannot arise as eventually periodic Fatou components of meromorphic functions