Local connectivity of boundaries of tame Fatou components of meromorphic functions

We consider holomorphic maps $f: U \rightarrow U$ for a hyperbolic domain $U$ in the complex plane, such that the iterates of $f$ converge to a boundary point $\zeta$ of $U$. By a previous result of the authors, for such maps there exist nice absorbing domains $W \subset U$. In this paper we show th...

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Detalles Bibliográficos
Autores: Barański, Krzysztof, Fagella Rabionet, Núria, Jarque i Ribera, Xavie, Karpińska, Bogusława
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2024
País:España
Institución:Universidad de Barcelona
Repositorio:Dipòsit Digital de la UB
OAI Identifier:oai:diposit.ub.edu:2445/216337
Acceso en línea:https://hdl.handle.net/2445/216337
Access Level:acceso abierto
Palabra clave:Sistemes dinàmics complexos
Funcions de variables complexes
Funcions meromorfes
Complex dynamical systems
Functions of complex variables
Meromorphic functions
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spelling Local connectivity of boundaries of tame Fatou components of meromorphic functionsBarański, KrzysztofFagella Rabionet, NúriaJarque i Ribera, XavieKarpińska, BogusławaSistemes dinàmics complexosFuncions de variables complexesFuncions meromorfesComplex dynamical systemsFunctions of complex variablesMeromorphic functionsWe consider holomorphic maps $f: U \rightarrow U$ for a hyperbolic domain $U$ in the complex plane, such that the iterates of $f$ converge to a boundary point $\zeta$ of $U$. By a previous result of the authors, for such maps there exist nice absorbing domains $W \subset U$. In this paper we show that $W$ can be chosen to be simply connected, if $f$ has doubly parabolic type in the sense of the Baker-Pommerenke-Cowen classification of its lift by a universal covering (and $\zeta$ is not an isolated boundary point of $U$). We also provide counterexamples for other types of the map $f$ and give an exact characterization of doubly parabolic type in terms of the dynamical behaviour of $f$.Springer Verlag2024info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://hdl.handle.net/2445/216337Articles publicats en revistes (Matemàtiques i Informàtica)reponame:Dipòsit Digital de la UBinstname:Universidad de BarcelonaInglésReproducció del document publicat a: https://doi.org/10.1007/s00208-024-02957-yMathematische Annalen, 2024https://doi.org/10.1007/s00208-024-02957-ycc by (c) Krzysztof Barańskit et al., 2024http://creativecommons.org/licenses/by/3.0/es/info:eu-repo/semantics/openAccessoai:diposit.ub.edu:2445/2163372026-05-27T06:46:51Z
dc.title.none.fl_str_mv Local connectivity of boundaries of tame Fatou components of meromorphic functions
title Local connectivity of boundaries of tame Fatou components of meromorphic functions
spellingShingle Local connectivity of boundaries of tame Fatou components of meromorphic functions
Barański, Krzysztof
Sistemes dinàmics complexos
Funcions de variables complexes
Funcions meromorfes
Complex dynamical systems
Functions of complex variables
Meromorphic functions
title_short Local connectivity of boundaries of tame Fatou components of meromorphic functions
title_full Local connectivity of boundaries of tame Fatou components of meromorphic functions
title_fullStr Local connectivity of boundaries of tame Fatou components of meromorphic functions
title_full_unstemmed Local connectivity of boundaries of tame Fatou components of meromorphic functions
title_sort Local connectivity of boundaries of tame Fatou components of meromorphic functions
dc.creator.none.fl_str_mv Barański, Krzysztof
Fagella Rabionet, Núria
Jarque i Ribera, Xavie
Karpińska, Bogusława
author Barański, Krzysztof
author_facet Barański, Krzysztof
Fagella Rabionet, Núria
Jarque i Ribera, Xavie
Karpińska, Bogusława
author_role author
author2 Fagella Rabionet, Núria
Jarque i Ribera, Xavie
Karpińska, Bogusława
author2_role author
author
author
dc.subject.none.fl_str_mv Sistemes dinàmics complexos
Funcions de variables complexes
Funcions meromorfes
Complex dynamical systems
Functions of complex variables
Meromorphic functions
topic Sistemes dinàmics complexos
Funcions de variables complexes
Funcions meromorfes
Complex dynamical systems
Functions of complex variables
Meromorphic functions
description We consider holomorphic maps $f: U \rightarrow U$ for a hyperbolic domain $U$ in the complex plane, such that the iterates of $f$ converge to a boundary point $\zeta$ of $U$. By a previous result of the authors, for such maps there exist nice absorbing domains $W \subset U$. In this paper we show that $W$ can be chosen to be simply connected, if $f$ has doubly parabolic type in the sense of the Baker-Pommerenke-Cowen classification of its lift by a universal covering (and $\zeta$ is not an isolated boundary point of $U$). We also provide counterexamples for other types of the map $f$ and give an exact characterization of doubly parabolic type in terms of the dynamical behaviour of $f$.
publishDate 2024
dc.date.none.fl_str_mv 2024
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/2445/216337
url https://hdl.handle.net/2445/216337
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Reproducció del document publicat a: https://doi.org/10.1007/s00208-024-02957-y
Mathematische Annalen, 2024
https://doi.org/10.1007/s00208-024-02957-y
dc.rights.none.fl_str_mv cc by (c) Krzysztof Barańskit et al., 2024
http://creativecommons.org/licenses/by/3.0/es/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv cc by (c) Krzysztof Barańskit et al., 2024
http://creativecommons.org/licenses/by/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Springer Verlag
publisher.none.fl_str_mv Springer Verlag
dc.source.none.fl_str_mv Articles publicats en revistes (Matemàtiques i Informàtica)
reponame:Dipòsit Digital de la UB
instname:Universidad de Barcelona
instname_str Universidad de Barcelona
reponame_str Dipòsit Digital de la UB
collection Dipòsit Digital de la UB
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,81155

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