Web of Science: 2 cites, Scopus: 2 cites, Google Scholar: cites
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)

Data: 2015
Resum: 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.
Nota: 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.
Drets: Tots els drets reservats.
Llengua: Anglès.
Document: article ; recerca ; submittedVersion
Matèria: Entire maps ; Holomorphic dynamics ; Quasiconformal maps ; Wandering domains
Publicat a: Journal of Mathematical Analysis and Applications, Vol. 429 (2015) , p. 478-496, ISSN 0022-247X

DOI: 10.1016/j.jmaa.2015.04.020

21 p, 637.0 KB

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Documents de recerca > Documents dels grups de recerca de la UAB > Centres i grups de recerca (producció científica) > Ciències > GSD (Grup de sistemes dinàmics)
Articles > Articles de recerca
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 Registre creat el 2016-01-12, darrera modificació el 2019-03-07

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