Bounded Fatou and Julia components of meromorphic functions

IF 1.3 2区数学 Q1 MATHEMATICS

Mathematische Annalen Pub Date : 2024-06-08 DOI:10.1007/s00208-023-02725-4

David Martí-Pete, Lasse Rempe, James Waterman

引用次数: 0

Abstract

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.

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有界法图和非定常函数的 Julia 分量

我们完整地描述了有界集的特征，这些有界集是作为非定常函数的 Fatou 集和 Julia 集的组成部分出现的。一方面，我们证明当且仅当一个有界域是正则时，它才是某个微函数的法图分量。另一方面，我们证明，当且仅当一个平面连续体具有空内部时，它是某个分形函数的 Julia 分集。为此，我们利用近似理论构造了具有游走紧凑性的非定常函数。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematische Annalen 数学-数学

CiteScore

2.90

自引率

7.10%

发文量

181

审稿时长

4-8 weeks

期刊介绍： Begründet 1868 durch Alfred Clebsch und Carl Neumann. Fortgeführt durch Felix Klein, David Hilbert, Otto Blumenthal, Erich Hecke, Heinrich Behnke, Hans Grauert, Heinz Bauer, Herbert Amann, Jean-Pierre Bourguignon, Wolfgang Lück und Nigel Hitchin. The journal Mathematische Annalen was founded in 1868 by Alfred Clebsch and Carl Neumann. It was continued by Felix Klein, David Hilbert, Otto Blumenthal, Erich Hecke, Heinrich Behnke, Hans Grauert, Heinz Bauer, Herbert Amann, Jean-Pierre Bourguigon, Wolfgang Lück and Nigel Hitchin. Since 1868 the name Mathematische Annalen stands for a long tradition and high quality in the publication of mathematical research articles. Mathematische Annalen is designed not as a specialized journal but covers a wide spectrum of modern mathematics.