Absorbing sets and Baker domains for holomorphic maps

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 connec...

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Autores: Barański, Krzysztof, Fagella, Núria|||0000-0002-5466-0579, Jarque i Ribera, Xavier|||0000-0002-6576-9780, Karpinska, Boguslawa
Formato: artículo
Fecha de publicación:2014
País:España
Recursos:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:150689
Acesso em linha:https://ddd.uab.cat/record/150689
https://dx.doi.org/urn:doi:10.1112/jlms/jdv016
Access Level:acceso abierto
Palavra-chave:Baker domain
Hyperbolic domain
Hyperbolic measure
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spelling Absorbing sets and Baker domains for holomorphic mapsBarański, KrzysztofFagella, Núria|||0000-0002-5466-0579Jarque i Ribera, Xavier|||0000-0002-6576-9780Karpinska, BoguslawaBaker domainHyperbolic domainHyperbolic measureWe 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. 22014-01-0120142014-01-01Articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/150689https://dx.doi.org/urn:doi:10.1112/jlms/jdv016reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengAgència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2009/SGR-792Ministerio de Ciencia e Innovación https://doi.org/10.13039/501100004837 MTM2011-26995-C02-01open accesshttp://purl.org/coar/access_right/c_abf2Aquest material està protegit per drets d'autor i/o drets afins. Podeu utilitzar aquest material en funció del que permet la legislació de drets d'autor i drets afins d'aplicació al vostre cas. Per a d'altres usos heu d'obtenir permís del(s) titular(s) de drets.https://rightsstatements.org/vocab/InC/1.0/info:eu-repo/semantics/openAccessoai:ddd.uab.cat:1506892026-06-06T12:50:31Z
dc.title.none.fl_str_mv Absorbing sets and Baker domains for holomorphic maps
title Absorbing sets and Baker domains for holomorphic maps
spellingShingle Absorbing sets and Baker domains for holomorphic maps
Barański, Krzysztof
Baker domain
Hyperbolic domain
Hyperbolic measure
title_short Absorbing sets and Baker domains for holomorphic maps
title_full Absorbing sets and Baker domains for holomorphic maps
title_fullStr Absorbing sets and Baker domains for holomorphic maps
title_full_unstemmed Absorbing sets and Baker domains for holomorphic maps
title_sort Absorbing sets and Baker domains for holomorphic maps
dc.creator.none.fl_str_mv Barański, Krzysztof
Fagella, Núria|||0000-0002-5466-0579
Jarque i Ribera, Xavier|||0000-0002-6576-9780
Karpinska, Boguslawa
author Barański, Krzysztof
author_facet Barański, Krzysztof
Fagella, Núria|||0000-0002-5466-0579
Jarque i Ribera, Xavier|||0000-0002-6576-9780
Karpinska, Boguslawa
author_role author
author2 Fagella, Núria|||0000-0002-5466-0579
Jarque i Ribera, Xavier|||0000-0002-6576-9780
Karpinska, Boguslawa
author2_role author
author
author
dc.subject.none.fl_str_mv Baker domain
Hyperbolic domain
Hyperbolic measure
topic Baker domain
Hyperbolic domain
Hyperbolic measure
description 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.
publishDate 2014
dc.date.none.fl_str_mv 2
2014-01-01
2014
2014-01-01
dc.type.none.fl_str_mv Article
http://purl.org/coar/resource_type/c_6501
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://ddd.uab.cat/record/150689
https://dx.doi.org/urn:doi:10.1112/jlms/jdv016
url https://ddd.uab.cat/record/150689
https://dx.doi.org/urn:doi:10.1112/jlms/jdv016
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2009/SGR-792
Ministerio de Ciencia e Innovación https://doi.org/10.13039/501100004837 MTM2011-26995-C02-01
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://rightsstatements.org/vocab/InC/1.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
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https://rightsstatements.org/vocab/InC/1.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Dipòsit Digital de Documents de la UAB
instname:Universitat Autònoma de Barcelona
instname_str Universitat Autònoma de Barcelona
reponame_str Dipòsit Digital de Documents de la UAB
collection Dipòsit Digital de Documents de la UAB
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