Wandering domains for composition of entire functions
Fagella Rabionet, Núria (Universitat de Barcelona. Departament de Matemàtica Aplicada i Anàlisi)
Godillon, Sebastién (Universitat de Barcelona. Institut de Matemàtiques)
Jarque i Ribera, Xavier (Universitat Rovira i Virgili. Departament d'Enginyeria Informàtica i Matemàtiques)

Date:	2015
Abstract:	C. ~Bishop constructs an example of an entire function f in class B with at least two grand orbits of oscillating wandering domains. In this paper we show that his example has exactly two such orbits, that is, f has no unexpected wandering domains. We apply this result to the classical problem of relating the Julia sets of composite functions with the Julia set of its members. More precisely, we show the existence of two entire maps f and g in class B such that the Fatou set of f g has a wandering domain, while all Fatou components of f or g are preperiodic. This complements a result of A. ~Singh and results of W. ~Bergweiler and A. Hinkkanen related to this problem.
Note:	Agraïments: We heartfully thank Chris Bishop for his patience and kindness in answering all our questions about his remarkable result. We also wish to thank Lasse Rempe, Phil Rippon, Gwyneth Stallard and Toni Garijo for many helpful discussions. The second author also wants to thank the Institut de Matemàtiques de la Universitat de Barcelona (IMUB) for its hospitality while the work was carried out.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Entire maps ; Holomorphic dynamics ; Quasiconformal maps ; Wandering domains
Published in:	Journal of mathematical analysis and applications, Vol. 429 (2015) , p. 478-496, ISSN 1096-0813

DOI: 10.1016/j.jmaa.2015.04.020

Postprint 21 p, 637.0 KB

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