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Title: | Fatou components and singularities of meromorphic functions |
Author: | Baranski, Krzysztof Fagella Rabionet, Núria Jarque i Ribera, Xavier Karpinska, Boguslawa |
Keywords: | Equacions funcionals Funcions analítiques Sistemes dinàmics complexos Polinomis Funcions enteres Funcions meromorfes Functional equations Analytic functions Complex dynamical systems Polynomials Entire functions Meromorphic functions |
Issue Date: | Apr-2020 |
Publisher: | Cambridge University Press |
Abstract: | We prove several results concerning the relative position of points in the postsingular set $P(f)$ of a meromorphic map $f$ and the boundary of a Baker domain or the successive iterates of a wandering component. For Baker domains we answer a question of Mihaljevi\'c-Brandt and Rempe-Gillen. For wandering domains we show that if the iterates $U_n$ of such a domain have uniformly bounded diameter, then there exists a sequence of postsingular values $p_n$ such that $\dist(p_n, U_n)\to 0$ as $n\to \infty$. We also prove that if $U_n \cap P(f)=\emptyset$ and the postsingular set of $f$ lies at a positive distance from the Julia set (in $\C$), then the sequence of iterates of any wandering domain must contain arbitrarily large disks. This allows to exclude the existence of wandering domains for some meromorphic maps with infinitely many poles and unbounded set of singular values. |
Note: | Versió postprint del document publicat a: https://doi.org/10.1017/prm.2018.142 |
It is part of: | Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2020, vol. 150, num. 2, p. 633-654 |
URI: | http://hdl.handle.net/2445/130195 |
Related resource: | https://doi.org/10.1017/prm.2018.142 |
ISSN: | 0308-2105 |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
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