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Journal of the London Mathematical Society 2000 62(1):139-148; doi:10.1112/S0024610700001149
© 2000 by London Mathematical Society
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© The London Mathematical Society

Repulsive Fixpoints of Analytic Functions with Applications to Complex Dynamics

Matts Essén and Shengjian Wu

Department of Mathematics, Uppsala University Box 480, S-75106 Uppsala, Sweden, matts{at}math.uu.se
Department of Mathematics, Peking University Beijing 100871, China, wusj{at}pku.edu.cn

Received 12 February 1999. Revision received 21 June 1999.

Let G be a family of functions analytic in a domain D in the complex plane. It is proved that G is a normal family, provided that for each fisinG, 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.


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