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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: https://doi.org/10.1112/jlms/jdv016 |
It is part of: | Journal of the London Mathematical Society-Second Series, 2015, vol. 92, num. 1, p. 144-162 |
URI: | http://hdl.handle.net/2445/164104 |
Related resource: | https://doi.org/10.1112/jlms/jdv016 |
ISSN: | 0024-6107 |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
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