Distributional chaos for linear operators

We characterize distributional chaos for linear operators on Fréchet spaces in terms of a computable condition (DCC), and also as the existence of distributionally irregular vectors. A sufficient condition for the existence of dense uniformly distributionally irregular manifolds is presented, which...

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Autores: Bernardes, Nilson C., Bonilla, Antonio, Müller, Vladimír, Peris Manguillot, Alfredo|||0000-0003-1683-2373
Tipo de recurso: artículo
Fecha de publicación:2013
País:España
Institución:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/43115
Acceso en línea:https://riunet.upv.es/handle/10251/43115
Access Level:acceso abierto
Palabra clave:Distributional chaos
Irregular vectors
Chaotic operators
Frequently hypercyclic operators
Point spectrum
Invariant
MATEMATICA APLICADA
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spelling Distributional chaos for linear operatorsBernardes, Nilson C.Bonilla, AntonioMüller, VladimírPeris Manguillot, Alfredo|||0000-0003-1683-2373Distributional chaosIrregular vectorsChaotic operatorsFrequently hypercyclic operatorsPoint spectrumInvariantMATEMATICA APLICADAWe characterize distributional chaos for linear operators on Fréchet spaces in terms of a computable condition (DCC), and also as the existence of distributionally irregular vectors. A sufficient condition for the existence of dense uniformly distributionally irregular manifolds is presented, which is very general and can be applied to many classes of operators. Distributional chaos is also analyzed in connection with frequent hypercyclicity, and the particular cases of weighted shifts and composition operators are given as an illustration of the previous results. © 2013 Elsevier Inc.The fourth author was supported in part by MEC and FEDER, Project MTM2010-14909.ElsevierDepartamento de Matemática AplicadaEscuela Técnica Superior de ArquitecturaInstituto Universitario de Matemática Pura y AplicadaEuropean Regional Development FundMinisterio de Ciencia e InnovaciónRepositorio Institucional de la Universitat Politècnica de València Riunet20132013-11-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfapplication/pdfhttps://riunet.upv.es/handle/10251/43115reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)InglésengMinisterio de Ciencia e Innovación http://dx.doi.org/10.13039/501100004837 MTM2010-14909 HIPERCICLICIDAD Y CAOS DE OPERADORESopen accesshttp://purl.org/coar/access_right/c_abf2Reserva de todos los derechoshttp://rightsstatements.org/vocab/InC/1.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/431152026-06-13T07:49:27Z
dc.title.none.fl_str_mv Distributional chaos for linear operators
title Distributional chaos for linear operators
spellingShingle Distributional chaos for linear operators
Bernardes, Nilson C.
Distributional chaos
Irregular vectors
Chaotic operators
Frequently hypercyclic operators
Point spectrum
Invariant
MATEMATICA APLICADA
title_short Distributional chaos for linear operators
title_full Distributional chaos for linear operators
title_fullStr Distributional chaos for linear operators
title_full_unstemmed Distributional chaos for linear operators
title_sort Distributional chaos for linear operators
dc.creator.none.fl_str_mv Bernardes, Nilson C.
Bonilla, Antonio
Müller, Vladimír
Peris Manguillot, Alfredo|||0000-0003-1683-2373
author Bernardes, Nilson C.
author_facet Bernardes, Nilson C.
Bonilla, Antonio
Müller, Vladimír
Peris Manguillot, Alfredo|||0000-0003-1683-2373
author_role author
author2 Bonilla, Antonio
Müller, Vladimír
Peris Manguillot, Alfredo|||0000-0003-1683-2373
author2_role author
author
author
dc.contributor.none.fl_str_mv Departamento de Matemática Aplicada
Escuela Técnica Superior de Arquitectura
Instituto Universitario de Matemática Pura y Aplicada
European Regional Development Fund
Ministerio de Ciencia e Innovación
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Distributional chaos
Irregular vectors
Chaotic operators
Frequently hypercyclic operators
Point spectrum
Invariant
MATEMATICA APLICADA
topic Distributional chaos
Irregular vectors
Chaotic operators
Frequently hypercyclic operators
Point spectrum
Invariant
MATEMATICA APLICADA
description We characterize distributional chaos for linear operators on Fréchet spaces in terms of a computable condition (DCC), and also as the existence of distributionally irregular vectors. A sufficient condition for the existence of dense uniformly distributionally irregular manifolds is presented, which is very general and can be applied to many classes of operators. Distributional chaos is also analyzed in connection with frequent hypercyclicity, and the particular cases of weighted shifts and composition operators are given as an illustration of the previous results. © 2013 Elsevier Inc.
publishDate 2013
dc.date.none.fl_str_mv 2013
2013-11-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://riunet.upv.es/handle/10251/43115
url https://riunet.upv.es/handle/10251/43115
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Ministerio de Ciencia e Innovación http://dx.doi.org/10.13039/501100004837 MTM2010-14909 HIPERCICLICIDAD Y CAOS DE OPERADORES
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reserva de todos los derechos
http://rightsstatements.org/vocab/InC/1.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reserva de todos los derechos
http://rightsstatements.org/vocab/InC/1.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
instname:Universitat Politècnica de València (UPV)
instname_str Universitat Politècnica de València (UPV)
reponame_str RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
collection RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
repository.name.fl_str_mv
repository.mail.fl_str_mv
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