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.
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页码：451 / 462
页数：12
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