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ON THE UNIFORM PERFECTNESS OF THE BOUNDARY OF MULTIPLY CONNECTED WANDERING DOMAINS

Part of: Complex dynamical systems

Published online by Cambridge University Press:  04 November 2011

WALTER BERGWEILER  and
JIAN-HUA ZHENG
WALTER BERGWEILER*
Affiliation:
Mathematisches Seminar, Christian-Albrechts-Universität zu Kiel, Ludewig-Meyn-Str. 4, D–24098 Kiel, Germany (email: bergweiler@math.uni-kiel.de)
JIAN-HUA ZHENG
Affiliation:
Department of Mathematical Sciences, Tsinghua University, 100084, Beijing, PR China (email: jzheng@math.tsinghua.edu.cn)
*
✉For correspondence; e-mail: bergweiler@math.uni-kiel.de
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Abstract

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We investigate when the boundary of a multiply connected wandering domain of an entire function is uniformly perfect. We give a general criterion implying that it is not uniformly perfect. This criterion applies in particular to examples of multiply connected wandering domains given by Baker. We also provide examples of infinitely connected wandering domains whose boundary is uniformly perfect.

Keywords

Fatou setJulia setiterationentire functionwandering domainuniformly perfect

MSC classification

Secondary: 37F10: Polynomials; rational maps; entire and meromorphic functions
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 91 , Issue 3 , December 2011 , pp. 289 - 311
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

Footnotes

The first-named author was supported by a Chinese Academy of Sciences Visiting Professorship for Senior International Scientists, Grant No. 2010 TIJ10, the Deutsche Forschungsgemeinschaft, Be 1508/7-1, the EU Research Training Network CODY and the ESF Networking Programme HCAA. The second-named author was supported by Grant No. 10871108 of the NSF of China.

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