Hyperbolic entire functions with bounded Fatou components
Bergweiler, Walter (Christian-Albrechts-Universität zu Kiel (Alemanya))
Fagella Rabionet, Núria (Universitat de Barcelona. Departament de Matemàtica Aplicada i Anàlisi)
Rempe, Lasse (University of Liverpool(UK). Dept. of Mathematical Sciences)

Date:	2015
Abstract:	We show that an invariant Fatou component of a hyperbolic transcendental entire function is a Jordan domain (in fact, a quasidisc) if and only if it contains only finitely many critical points and no asymptotic curves. We use this theorem to prove criteria for the boundedness of Fatou components and local connectivity of Julia sets for hyperbolic entire functions, and give examples that demonstrate that our results are optimal. A particularly strong dichotomy is obtained in the case of a function with precisely two critical values.
Grants:	Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-792 Ministerio de Economía y Competitividad MTM2011-26995-C02-02
Note:	Agraïments: The third author was supported by a Philip Leverhulme Prize.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Axiom A ; Bounded Fatou component ; Eremenko-Lyubich class ; Fatou set ; Hyperbolicity ; Jordan curve ; Julia set ; Laguerre-Pólya class ; Local connectivity ; Quasicircle ; Quasidisc ; Transcendental entire function
Published in:	Commentarii Mathematici Helvetici. A Journal of the Swiss Mathematical Society, Vol. 90 Núm. 4 (2015) , p. 799-829, ISSN 0010-2571

Postprint 27 p, 2.8 MB

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