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2015-06-10

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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/164104

Absorbing sets and Baker domains for holomorphic maps

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https://doi.org/10.1112/jlms/jdv016

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 $f$.

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Funcions de variables complexes, Funcions meromorfes, Sistemes dinàmics complexos

Subject (English)

Functions of complex variables, Meromorphic functions, Complex dynamical systems

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Articles publicats en revistes (Matemàtiques i Informàtica)

Citation

BARANSKI, Krzysztof, et al. Absorbing sets and Baker domains for holomorphic maps. Journal of the London Mathematical Society-Second Series. 2015. Vol. 92, num. 1, pags. 144-162. ISSN 0024-6107. [consulted: 7 of August of 2026]. Available at: https://hdl.handle.net/2445/164104

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