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On the Hausdorff dimension of the Julia set of a regularly growing entire function†

Published online by Cambridge University Press:  15 January 2010

WALTER BERGWEILER  and
BOGUSŁAWA KARPIŃSKA
WALTER BERGWEILER
Affiliation:
Mathematisches Seminar, Christian–Albrechts–Universität zu Kiel, Ludewig–Meyn–Str. 4, D–24098 Kiel, Germany. e-mail: bergweiler@math.uni-kiel.de
BOGUSŁAWA KARPIŃSKA
Affiliation:
Faculty of Mathematics and Information Science, Warsaw University of Technology, Pl. Politechniki 1, 00-661 Warszawa, Poland. e-mail: bkarpin@mini.pw.edu.pl
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Abstract

We show that if the growth of a transcendental entire function f is sufficiently regular, then the Julia set and the escaping set of f have Hausdorff dimension 2.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 148 , Issue 3 , May 2010 , pp. 531 - 551
Copyright
Copyright © Cambridge Philosophical Society 2010

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