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

页码：95 / 111

页数：17

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