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Title of Journal: Math Ann

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Abbravation: Mathematische Annalen

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Springer Berlin Heidelberg

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DOI

10.1007/bf02710454

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1432-1807

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Absence of wandering domains for some real entire

Authors: Helena MihaljevićBrandt Lasse RempeGillen
Publish Date: 2013/06/29
Volume: 357, Issue: 4, Pages: 1577-1604
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Abstract

Let f be a real entire function whose set Sf of singular values is real and bounded We show that if f satisfies a certain functiontheoretic condition the “sector condition” then f has no wandering domains Our result includes all maps of the form zmapsto lambda fracsinh zz + a with lambda 0 and ain mathbbR We also show the absence of wandering domains for certain nonreal entire functions for which Sf is bounded and fn Sfrightarrow infty uniformly As a special case of our theorem we give a short elementary and nontechnical proof that the Julia set of the exponential map fz=ez is the entire complex plane Furthermore we apply similar methods to extend a result of Bergweiler concerning Baker domains of entire functions and their relation to the postsingular set to the case of meromorphic functionsH MihaljevićBrandt and L RempeGillen were supported by EPSRC grant EP/E017886/1 L RempeGillen was supported by EPSRC Fellowship EP/E052851/1 H MihaljevićBrandt and L RempeGillen gratefully acknowledge support received through the European CODY network

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