On the connectivity of Julia sets of meromorphic functions
Barański, Krzysztof (University of Warsaw(Poland). Institute of Mathematics)
Fagella Rabionet, Núria (Universitat de Barcelona. Departament de Matemàtica Aplicada i Anàlisi)
Jarque i Ribera, Xavier (Universitat de Barcelona. Departament de Matemàtica Aplicada i Anàlisi)
Karpinska, Boguslawa (Warsaw University of Technology(Poland). Faculty of Mathematics and Information Science)

Date:	2014
Abstract:	We prove that every transcendental meromorphic map f with disconnected Julia set has a weakly repelling fixed point. This implies that the Julia set of Newton's method for finding zeroes of an entire map is connected. Moreover, extending a result of Cowen for holomorphic self-maps of the disc, we show the existence of absorbing domains for holomorphic self-maps of hyperbolic regions, whose iterates tend to a boundary point. In particular, the results imply that periodic Baker domains of Newton's method for entire maps are simply connected, which solves a well-known open question.
Grants:	Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-792 Ministerio de Economía y Competitividad MTM-2006-05849
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Absorbing domains ; Meromorphic functions ; Newton maps
Published in:	Inventiones Mathematicae, Vol. 198 Núm. 3 (2014) , p. 591-636, ISSN 1432-1297

DOI: 10.1007/s00222-014-0504-5

Postprint 34 p, 476.4 KB

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