Title:
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Absorbing sets and Baker domains for holomorphic maps
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Author:
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Barański, Krzysztof; Fagella Rabionet, Núria; Jarque i Ribera, Xavier; Karpinska, Boguslawa
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Abstract:
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Agraïments: Supported by Polish NCN grant decision DEC-2012/06/M/ST1/00168 |
Abstract:
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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. |
Subject(s):
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-Baker domain -Hyperbolic domain -Hyperbolic measure |
Rights:
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open access
Tots els drets reservats.
https://rightsstatements.org/vocab/InC/1.0/ |
Document type:
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Article |
Published by:
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Share:
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Uri:
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https://ddd.uab.cat/record/150689
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