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Absorbing sets and Baker domains for holomorphic maps
Baranski, Krzysztof
Fagella Rabionet, Núria
Jarque i Ribera, Xavier
Karpinska, Boguslawa

Data: 2014
Resum: 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.
Drets: Tots els drets reservats.
Llengua: Anglès
Document: article ; recerca ; preprint
Matèria: Baker domain ; hyperbolic domain ; hyperbolic measure
Publicat a: Journal of the London Mathematical Society. Second Series, Vol. 92 Núm. 1 (2014) , p. 144-162

DOI: 10.1112/jlms/jdv016

20 p, 347.6 KB

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