Absence of wandering domains for some real entire functions with bounded singular sets

作者：Mihaljevic Brandt Helena; Rempe Gillen Lasse^*

来源：Mathematische Annalen, 2013, 357(4): 1577-1604.

DOI：10.1007/s00208-013-0936-z

Let be a real entire function whose set of singular values is real and bounded. We show that, if satisfies a certain function-theoretic condition (the %26quot;sector condition%26quot;), then has no wandering domains. Our result includes all maps of the form with and . We also show the absence of wandering domains for certain non-real entire functions for which is bounded and uniformly. As a special case of our theorem, we give a short, elementary and non-technical proof that the Julia set of the exponential map 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 functions.

• 出版日期2013-12