Wandering domains for composition of entire functions

被引：13

作者：

Fagella, Nuria ^{[1
]}

Godillon, Sebastian ^{[2
]}

Jarque, Xavier ^{[1
]}

机构：

[1] Univ Barcelona, Dept Matemat Aplicada & Anal, E-08007 Barcelona, Spain

[2] Univ Barcelona, Inst Matemat, E-08007 Barcelona, Spain

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2015年 / 429卷 / 01期

关键词：

Quasiconformal maps; Wandering domains; Entire maps; Holomorphic dynamics; DYNAMICS; ITERATION; EXAMPLES;

D O I：

10.1016/j.jmaa.2015.04.020

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

C. Bishop in [10, Theorem 17.1] constructs an example of an entire function f in class B with at least two grand orbits of oscillating wandering domains. In this paper we show that his example has exactly two such orbits, that is, f has no unexpected wandering domains. We apply this result to the classical problem of relating the Julia sets of composite functions with the Julia set of its members. More precisely, we show the existence of two entire maps f and g in class B such that the Fatou set of f o g has a wandering domain, while all Fatou components of f or g are preperiodic. This complements a result of A. Singh in [22, Theorem 4] and results of W. Bergweiler and A. Hinkkanen in [6] related to this problem. (C) 2015 Elsevier Inc. All rights reserved.

引用

页码：478 / 496

页数：19

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