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Pàgina inicial > Articles > Articles publicats > Absorbing sets and Baker domains for holomorphic maps |
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. |
Ajuts: | Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-792 Ministerio de Ciencia e Innovación MTM2011-26995-C02-01 |
Nota: | Agraïments: Supported by Polish NCN grant decision DEC-2012/06/M/ST1/00168 |
Drets: | Tots els drets reservats. |
Llengua: | Anglès |
Document: | Article ; recerca ; Versió acceptada per publicar |
Matèria: | Baker domain ; Hyperbolic domain ; Hyperbolic measure |
Publicat a: | Journal of the London Mathematical Society, Vol. 92 Núm. 1 (2014) , p. 144-162, ISSN 1469-7750 |
Postprint 20 p, 347.6 KB |