On the connectivity of the escaping set for complex exponential Misiurewicz parameters

Let $ E_{\lambda}(z)=\lambda {\rm exp}(z), \lambda\in \mathbb{C}$, be the complex exponential family. For all functions in the family there is a unique asymptotic value at 0 (and no critical values). For a fixed $ \lambda$, the set of points in $ \mathbb{C}$ with orbit tending to infinity is called...

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Detalles Bibliográficos
Autor: Jarque i Ribera, Xavier
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2011
País:España
Institución:Universidad de Barcelona
Repositorio:Dipòsit Digital de la UB
OAI Identifier:oai:diposit.ub.edu:2445/51504
Acceso en línea:https://hdl.handle.net/2445/51504
Access Level:acceso abierto
Palabra clave:Dinàmica
Funcions holomorfes
Dinàmica topològica
Dynamics
Holomorphic functions
Topological dynamics
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spelling On the connectivity of the escaping set for complex exponential Misiurewicz parametersJarque i Ribera, XavierDinàmicaFuncions holomorfesDinàmica topològicaDynamicsHolomorphic functionsTopological dynamicsLet $ E_{\lambda}(z)=\lambda {\rm exp}(z), \lambda\in \mathbb{C}$, be the complex exponential family. For all functions in the family there is a unique asymptotic value at 0 (and no critical values). For a fixed $ \lambda$, the set of points in $ \mathbb{C}$ with orbit tending to infinity is called the escaping set. We prove that the escaping set of $ E_{\lambda}$ with $ \lambda$ Misiurewicz (that is, a parameter for which the orbit of the singular value is strictly preperiodic) is a connected set.American Mathematical Society (AMS)2011info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://hdl.handle.net/2445/51504Articles publicats en revistes (Matemàtiques i Informàtica)reponame:Dipòsit Digital de la UBinstname:Universidad de BarcelonaInglésReproducció del document publicat a: http://dx.doi.org/10.1090/S0002-9939-2010-10611-1Proceedings of the American Mathematical Society, 2011, vol. 139, num. 6, p. 2057-2065http://dx.doi.org/10.1090/S0002-9939-2010-10611-1(c) American Mathematical Society (AMS), 2011info:eu-repo/semantics/openAccessoai:diposit.ub.edu:2445/515042026-05-27T06:46:51Z
dc.title.none.fl_str_mv On the connectivity of the escaping set for complex exponential Misiurewicz parameters
title On the connectivity of the escaping set for complex exponential Misiurewicz parameters
spellingShingle On the connectivity of the escaping set for complex exponential Misiurewicz parameters
Jarque i Ribera, Xavier
Dinàmica
Funcions holomorfes
Dinàmica topològica
Dynamics
Holomorphic functions
Topological dynamics
title_short On the connectivity of the escaping set for complex exponential Misiurewicz parameters
title_full On the connectivity of the escaping set for complex exponential Misiurewicz parameters
title_fullStr On the connectivity of the escaping set for complex exponential Misiurewicz parameters
title_full_unstemmed On the connectivity of the escaping set for complex exponential Misiurewicz parameters
title_sort On the connectivity of the escaping set for complex exponential Misiurewicz parameters
dc.creator.none.fl_str_mv Jarque i Ribera, Xavier
author Jarque i Ribera, Xavier
author_facet Jarque i Ribera, Xavier
author_role author
dc.subject.none.fl_str_mv Dinàmica
Funcions holomorfes
Dinàmica topològica
Dynamics
Holomorphic functions
Topological dynamics
topic Dinàmica
Funcions holomorfes
Dinàmica topològica
Dynamics
Holomorphic functions
Topological dynamics
description Let $ E_{\lambda}(z)=\lambda {\rm exp}(z), \lambda\in \mathbb{C}$, be the complex exponential family. For all functions in the family there is a unique asymptotic value at 0 (and no critical values). For a fixed $ \lambda$, the set of points in $ \mathbb{C}$ with orbit tending to infinity is called the escaping set. We prove that the escaping set of $ E_{\lambda}$ with $ \lambda$ Misiurewicz (that is, a parameter for which the orbit of the singular value is strictly preperiodic) is a connected set.
publishDate 2011
dc.date.none.fl_str_mv 2011
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/2445/51504
url https://hdl.handle.net/2445/51504
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Reproducció del document publicat a: http://dx.doi.org/10.1090/S0002-9939-2010-10611-1
Proceedings of the American Mathematical Society, 2011, vol. 139, num. 6, p. 2057-2065
http://dx.doi.org/10.1090/S0002-9939-2010-10611-1
dc.rights.none.fl_str_mv (c) American Mathematical Society (AMS), 2011
info:eu-repo/semantics/openAccess
rights_invalid_str_mv (c) American Mathematical Society (AMS), 2011
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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score 15,300719

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