Permutable entire functions and multiply connected wandering domains

被引：7

作者：

Benini, Anna Miriam ^{[1
]}

Rippon, Philip J. ^{[2
]}

Stallard, Gwyneth M. ^{[2
]}

机构：

[1] Univ Roma Tor Vergata, Dipartimento Matemat, V Ric Sci 1, I-00133 Rome, Italy

[2] Open Univ, Dept Math & Stat, Walton Hall, Milton Keynes MK7 6AA, Bucks, England

来源：

ADVANCES IN MATHEMATICS | 2016年 / 287卷

基金：

英国工程与自然科学研究理事会;

关键词：

Transcendental entire function; Julia set; Permutable functions; Multiply connected wandering domain; Fast escaping set; ITERATION; FATOU;

D O I：

10.1016/j.aim.2015.04.031

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let f and g be permutable transcendental entire functions. We use a recent analysis of the dynamical behavior in multiply connected wandering domains to make progress on the long standing conjecture that the Julia sets of f and g are equal; in particular, we show that J(f) = J(g) provided that neither f nor g has a simply connected wandering domain in the fast escaping set. (C) 2015 Elsevier Inc. All rights reserved.

引用

页码：451 / 462

页数：12

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