Bounded Fatou and Julia components of meromorphic functions

被引：0
|
作者：
Marti-Pete, David [1 ]
Rempe, Lasse [1 ]
Waterman, James [2 ]
机构：
[1] Univ Liverpool, Dept Math Sci, Liverpool L69 7ZL, England
[2] SUNY Stony Brook, Inst Math Sci, Stony Brook, NY 11794 USA
来源：
MATHEMATISCHE ANNALEN | 2025年 / 391卷 / 01期
关键词：
Primary; 37F10; Secondary; 30D05; 37B45; 54F15; CONNECTED WANDERING DOMAINS; ITERATION; DYNAMICS;
D O I：
10.1007/s00208-023-02725-4
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We completely characterise the bounded sets that arise as components of the Fatou and Julia sets of meromorphic functions. On the one hand, we prove that a bounded domain is a Fatou component of some meromorphic function if and only if it is regular. On the other hand, we prove that a planar continuum is a Julia component of some meromorphic function if and only if it has empty interior. We do so by constructing meromorphic functions with wandering compacta using approximation theory.
引用
收藏
页码：95 / 111
页数：17
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