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Entire functions with Julia sets of zero measure

Published online by Cambridge University Press:  24 October 2008

Gwyneth M. Stallard
Gwyneth M. Stallard
Affiliation:
Department of Mathematics, Imperial College of Science and Technology, London SW7 2BZ
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Abstract

We extend results of McMullen about the dynamics of entire functions for which the orbits of the critical values stay away from the Julia set. In particular we show that such functions are expanding on their Julia sets which have self-similarity properties. Under suitable further conditions the Julia sets have plane measure zero.

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 108 , Issue 3 , November 1990 , pp. 551 - 557
Copyright
Copyright © Cambridge Philosophical Society 1990

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