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REPULSIVE FIXPOINTS OF ANALYTIC FUNCTIONS WITH APPLICATIONS TO COMPLEX DYNAMICS

Published online by Cambridge University Press:  30 October 2000

MATTS ESSÉN  and
SHENGJIAN WU
MATTS ESSÉN
Affiliation:
Department of Mathematics, Uppsala University, Box 480, S-75106 Uppsala, Sweden; matts@math.uu.se
SHENGJIAN WU
Affiliation:
Department of Mathematics, Peking University, Beijing 100871, China; wusj@pku.edu.cn
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Abstract

Let [Gscr ] be a family of functions analytic in a domain D in the complex plane. It is proved that [Gscr ] is a normal family, provided that for each f∈[Gscr ], there exists k = k(f) > 1 such that the kth iterate fk has no repulsive fixpoint in D. A new proof of a result of Bergweiler and Terglane concerning the dynamics of entire functions is also given.

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 62 , Issue 1 , August 2000 , pp. 139 - 148
Copyright
The London Mathematical Society 2000

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