Title:
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Fatou components and singularities of meromorphic functions
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Author:
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Baranski, Krzysztof; Fagella Rabionet, Núria; Jarque i Ribera, Xavier; Karpinska, Boguslawa
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Other authors:
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Universitat de Barcelona |
Abstract:
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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. |
Subject(s):
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-Equacions funcionals -Funcions analítiques -Sistemes dinàmics complexos -Polinomis -Funcions enteres -Funcions meromorfes -Functional equations -Analytic functions -Complex dynamical systems -Polynomials -Entire functions -Meromorphic functions |
Rights:
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(c) Royal Society of Edinburgh , 2018
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Document type:
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Article Article - Accepted version |
Published by:
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Cambridge University Press
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