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Title: Absorbing sets and Baker domains for holomorphic maps
Author: Baranski, Krzysztof
Fagella Rabionet, Núria
Jarque i Ribera, Xavier
Karpinska, Boguslawa
Keywords: Funcions de variables complexes
Funcions meromorfes
Sistemes dinàmics complexos
Functions of complex variables
Meromorphic functions
Complex dynamical systems
Issue Date: 10-Jun-2015
Publisher: London Mathematical Society
Abstract: We consider holomorphic maps $f: U \rightarrow U$ for a hyperbolic domain $U$ in the complex plane, such that the iterates of $f$ converge to a boundary point $\zeta$ of $U$. By a previous result of the authors, for such maps there exist nice absorbing domains $W \subset U$. In this paper we show that $W$ can be chosen to be simply connected, if $f$ has doubly parabolic type in the sense of the Baker-Pommerenke-Cowen classification of its lift by a universal covering (and $\zeta$ is not an isolated boundary point of $U$). We also provide counterexamples for other types of the map $f$ and give an exact characterization of doubly parabolic type in terms of the dynamical behaviour of $f$.
Note: Versió postprint del document publicat a:
It is part of: Journal of the London Mathematical Society-Second Series, 2015, vol. 92, num. 1, p. 144-162
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ISSN: 0024-6107
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

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