Hyperbolic entire functions with bounded Fatou components

We show that an invariant Fatou component of a hyperbolic transcenden- tal entire function is a Jordan domain (in fact, a quasidisc) if and only if it contains only finitely many critical points and no asymptotic curves. We use this theorem to prove criteria for the boundedness of Fatou components a...

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Autores: Bergweiler, Walter, Fagella Rabionet, Núria, Rempe-Gillen, Lasse
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2015
País:España
Institución:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositorio:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:2445/164120
Acceso en línea:https://hdl.handle.net/2445/164120
Access Level:acceso abierto
Palabra clave:Sistemes dinàmics complexos
Funcions de variables complexes
Complex dynamical systems
Functions of complex variables
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spelling Hyperbolic entire functions with bounded Fatou componentsBergweiler, WalterFagella Rabionet, NúriaRempe-Gillen, LasseSistemes dinàmics complexosFuncions de variables complexesComplex dynamical systemsFunctions of complex variablesWe show that an invariant Fatou component of a hyperbolic transcenden- tal entire function is a Jordan domain (in fact, a quasidisc) if and only if it contains only finitely many critical points and no asymptotic curves. We use this theorem to prove criteria for the boundedness of Fatou components and local connectivity of Julia sets for hyperbolic entire functions, and give examples that demonstrate that our re- sults are optimal. A particularly strong dichotomy is obtained in the case of a function with precisely two critical values.Springer Verlag2020202020152020info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersion31 p.application/pdfhttps://hdl.handle.net/2445/164120Articles publicats en revistes (Matemàtiques i Informàtica)reponame:Recercat. Dipósit de la Recerca de Catalunyainstname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)InglésVersió postprint del document publicat a: https://doi.org/10.4171/CMH/371Commentarii Mathematici Helvetici, 2015, vol. 90, num. 4, p. 799-829https://doi.org/10.4171/CMH/371(c) Springer Verlag, 2015info:eu-repo/semantics/openAccessoai:recercat.cat:2445/1641202026-05-29T05:05:01Z
dc.title.none.fl_str_mv Hyperbolic entire functions with bounded Fatou components
title Hyperbolic entire functions with bounded Fatou components
spellingShingle Hyperbolic entire functions with bounded Fatou components
Bergweiler, Walter
Sistemes dinàmics complexos
Funcions de variables complexes
Complex dynamical systems
Functions of complex variables
title_short Hyperbolic entire functions with bounded Fatou components
title_full Hyperbolic entire functions with bounded Fatou components
title_fullStr Hyperbolic entire functions with bounded Fatou components
title_full_unstemmed Hyperbolic entire functions with bounded Fatou components
title_sort Hyperbolic entire functions with bounded Fatou components
dc.creator.none.fl_str_mv Bergweiler, Walter
Fagella Rabionet, Núria
Rempe-Gillen, Lasse
author Bergweiler, Walter
author_facet Bergweiler, Walter
Fagella Rabionet, Núria
Rempe-Gillen, Lasse
author_role author
author2 Fagella Rabionet, Núria
Rempe-Gillen, Lasse
author2_role author
author
dc.subject.none.fl_str_mv Sistemes dinàmics complexos
Funcions de variables complexes
Complex dynamical systems
Functions of complex variables
topic Sistemes dinàmics complexos
Funcions de variables complexes
Complex dynamical systems
Functions of complex variables
description We show that an invariant Fatou component of a hyperbolic transcenden- tal entire function is a Jordan domain (in fact, a quasidisc) if and only if it contains only finitely many critical points and no asymptotic curves. We use this theorem to prove criteria for the boundedness of Fatou components and local connectivity of Julia sets for hyperbolic entire functions, and give examples that demonstrate that our re- sults are optimal. A particularly strong dichotomy is obtained in the case of a function with precisely two critical values.
publishDate 2015
dc.date.none.fl_str_mv 2015
2020
2020
2020
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/2445/164120
url https://hdl.handle.net/2445/164120
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/10.4171/CMH/371
Commentarii Mathematici Helvetici, 2015, vol. 90, num. 4, p. 799-829
https://doi.org/10.4171/CMH/371
dc.rights.none.fl_str_mv (c) Springer Verlag, 2015
info:eu-repo/semantics/openAccess
rights_invalid_str_mv (c) Springer Verlag, 2015
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 31 p.
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:Recercat. Dipósit de la Recerca de Catalunya
instname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
instname_str Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
reponame_str Recercat. Dipósit de la Recerca de Catalunya
collection Recercat. Dipósit de la Recerca de Catalunya
repository.name.fl_str_mv
repository.mail.fl_str_mv
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