Please use this identifier to cite or link to this item: http://hdl.handle.net/2445/164104
 Title: Absorbing sets and Baker domains for holomorphic maps Author: Baranski, KrzysztofFagella Rabionet, NúriaJarque i Ribera, XavierKarpinska, Boguslawa Keywords: Funcions de variables complexesFuncions meromorfesSistemes dinàmics complexosFunctions of complex variablesMeromorphic functionsComplex 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)

Files in This Item:
File Description SizeFormat