Absorbing sets and Baker domains for holomorphic maps
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 consider holomorphic maps f: U U for a hyperbolic domain U in the complex plane, such that the iterates of f converge to a boundary point of U. By a previous result of the authors, for such maps there exist nice absorbing domains W U. In this paper we show that W can be chosen to be simply connected, if f has parabolic~I type in the sense of the Baker--Pommerenke--Cowen classification of its lift by a universal covering (and is not an isolated boundary point of U). Moreover, we provide counterexamples for other types of the map f and give an exact characterization of parabolic~I type in terms of the dynamical behaviour of f.
Grants:	Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-792 Ministerio de Ciencia e Innovación MTM2011-26995-C02-01
Note:	Agraïments: Supported by Polish NCN grant decision DEC-2012/06/M/ST1/00168
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Baker domain ; Hyperbolic domain ; Hyperbolic measure
Published in:	Journal of the London Mathematical Society, Vol. 92 Núm. 1 (2014) , p. 144-162, ISSN 1469-7750

DOI: 10.1112/jlms/jdv016

Postprint 20 p, 347.6 KB

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