Accesses to infinity from Fatou components.

We study the boundary behaviour of a meromorphic map $f\mathbb{C} \rightarrow \widehat{C}$ on its invariant simply connected Fatou component $U$. To this aim, we develop the theory of accesses to boundary points of $U$ and their relation to the dynamics of $f$. In particular, we establish a correspo...

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Detalles Bibliográficos
Autores: Baranski, Krzysztof, Fagella Rabionet, Núria, Jarque i Ribera, Xavier, Karpinska, Boguslawa
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2017
País:España
Institución:Universidad de Barcelona
Repositorio:Dipòsit Digital de la UB
OAI Identifier:oai:diposit.ub.edu:2445/164087
Acceso en línea:https://hdl.handle.net/2445/164087
Access Level:acceso abierto
Palabra clave:Funcions meromorfes
Sistemes dinàmics complexos
Meromorphic functions
Complex dynamical systems
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spelling Accesses to infinity from Fatou components.Baranski, KrzysztofFagella Rabionet, NúriaJarque i Ribera, XavierKarpinska, BoguslawaFuncions meromorfesSistemes dinàmics complexosMeromorphic functionsComplex dynamical systemsWe study the boundary behaviour of a meromorphic map $f\mathbb{C} \rightarrow \widehat{C}$ on its invariant simply connected Fatou component $U$. To this aim, we develop the theory of accesses to boundary points of $U$ and their relation to the dynamics of $f$. In particular, we establish a correspondence between invariant accesses from $U$ to infinity or weakly repelling points of $f$ and boundary fixed points of the associated inner function on the unit disc. We apply our results to describe the accesses to infinity from invariant Fatou components of the Newton maps.American Mathematical Society (AMS)2017info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfhttps://hdl.handle.net/2445/164087Articles publicats en revistes (Matemàtiques i Informàtica)reponame:Dipòsit Digital de la UBinstname:Universidad de BarcelonaInglésVersió postprint del document publicat a: https://doi.org/10.1090/tran/6739Transactions of the American Mathematical Society, 2017, vol. 369, num. 3, p. 1835-1867https://doi.org/10.1090/tran/6739cc-by-nc-nd (c) American Mathematical Society (AMS), 2017http://creativecommons.org/licenses/by-nc-nd/3.0/esinfo:eu-repo/semantics/openAccessoai:diposit.ub.edu:2445/1640872026-05-27T06:46:51Z
dc.title.none.fl_str_mv Accesses to infinity from Fatou components.
title Accesses to infinity from Fatou components.
spellingShingle Accesses to infinity from Fatou components.
Baranski, Krzysztof
Funcions meromorfes
Sistemes dinàmics complexos
Meromorphic functions
Complex dynamical systems
title_short Accesses to infinity from Fatou components.
title_full Accesses to infinity from Fatou components.
title_fullStr Accesses to infinity from Fatou components.
title_full_unstemmed Accesses to infinity from Fatou components.
title_sort Accesses to infinity from Fatou components.
dc.creator.none.fl_str_mv Baranski, Krzysztof
Fagella Rabionet, Núria
Jarque i Ribera, Xavier
Karpinska, Boguslawa
author Baranski, Krzysztof
author_facet Baranski, Krzysztof
Fagella Rabionet, Núria
Jarque i Ribera, Xavier
Karpinska, Boguslawa
author_role author
author2 Fagella Rabionet, Núria
Jarque i Ribera, Xavier
Karpinska, Boguslawa
author2_role author
author
author
dc.subject.none.fl_str_mv Funcions meromorfes
Sistemes dinàmics complexos
Meromorphic functions
Complex dynamical systems
topic Funcions meromorfes
Sistemes dinàmics complexos
Meromorphic functions
Complex dynamical systems
description We study the boundary behaviour of a meromorphic map $f\mathbb{C} \rightarrow \widehat{C}$ on its invariant simply connected Fatou component $U$. To this aim, we develop the theory of accesses to boundary points of $U$ and their relation to the dynamics of $f$. In particular, we establish a correspondence between invariant accesses from $U$ to infinity or weakly repelling points of $f$ and boundary fixed points of the associated inner function on the unit disc. We apply our results to describe the accesses to infinity from invariant Fatou components of the Newton maps.
publishDate 2017
dc.date.none.fl_str_mv 2017
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/2445/164087
url https://hdl.handle.net/2445/164087
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Versió postprint del document publicat a: https://doi.org/10.1090/tran/6739
Transactions of the American Mathematical Society, 2017, vol. 369, num. 3, p. 1835-1867
https://doi.org/10.1090/tran/6739
dc.rights.none.fl_str_mv cc-by-nc-nd (c) American Mathematical Society (AMS), 2017
http://creativecommons.org/licenses/by-nc-nd/3.0/es
info:eu-repo/semantics/openAccess
rights_invalid_str_mv cc-by-nc-nd (c) American Mathematical Society (AMS), 2017
http://creativecommons.org/licenses/by-nc-nd/3.0/es
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv American Mathematical Society (AMS)
publisher.none.fl_str_mv American Mathematical Society (AMS)
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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