Fatou components and singularities of meromorphic functions
Barański, Krzysztof (University of Warsaw. Institute of Mathematics (Poland))
Fagella Rabionet, Núria (Universitat de Barcelona. Institut de Matemàtiques)
Jarque i Ribera, Xavier (Universitat de Barcelona. Institut de Matemàtiques)
Karpińska, Bogusława (Warsaw University of Technology (Poland))

Date:	2020
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 Mihaljević-Brandt and Rempe-Gillen. For wandering domains we show that if the iterates Un of such a domain have uniformly bounded diameter, then there exists a sequence of postsingular values pn such that dist(pn, Un) → 0 as n → ∞. We also prove that if Un∩P(f) = ∅ 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.
Grants:	Ministerio de Economía y Competitividad MTM2017-86795-C3-3-P Ministerio de Economía y Competitividad MDM-2014-0445 Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1374
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Transcendental dynamics ; Julia set ; Baker domain ; Wandering domain
Published in:	Proceedings of the Royal Society of Edinburgh Section A: Mathematics, Vol. 150, Issue 2 (April 2020) , p. 633-654, ISSN 1473-7124

DOI: 10.1017/prm.2018.142

Postprint 19 p, 594.1 KB

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