On the existence of polynomials with chaotic behaviour

We establish a general result on the existence of hypercyclic (resp., transitive, weakly mixing, mixing, frequently hypercyclic) polynomials on locally convex spaces. As a consequence we prove that every (real or complex) infinite-dimensional separable Frèchet space admits mixing (hence hypercyclic)...

Descripción completa

Detalles Bibliográficos
Autores: Bernardes, Nilson C., 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:10251/40690
Acceso en línea:https://riunet.upv.es/handle/10251/40690
Access Level:acceso abierto
Palabra clave:Topological vector-spaces
Hypercyclic polynomials
Hypercyclic operators
Distributional chaos
Linear-operators
Banach-Spaces
Mixing polynomials
Frequently hypercyclic polynomials
Chaotic polynomials
MATEMATICA APLICADA
id ES_b2cb4ea283d6c0683b3db4d682fcf5f9
oai_identifier_str oai:riunet.upv.es:10251/40690
network_acronym_str ES
network_name_str España
repository_id_str
spelling On the existence of polynomials with chaotic behaviourBernardes, Nilson C.Peris Manguillot, Alfredo|||0000-0003-1683-2373Topological vector-spacesHypercyclic polynomialsHypercyclic operatorsDistributional chaosLinear-operatorsBanach-SpacesMixing polynomialsFrequently hypercyclic polynomialsChaotic polynomialsMATEMATICA APLICADAWe establish a general result on the existence of hypercyclic (resp., transitive, weakly mixing, mixing, frequently hypercyclic) polynomials on locally convex spaces. As a consequence we prove that every (real or complex) infinite-dimensional separable Frèchet space admits mixing (hence hypercyclic) polynomials of arbitrary positive degree. Moreover, every complex infinite-dimensional separable Banach space with an unconditional Schauder decomposition and every complex Frèchet space with an unconditional basis support chaotic and frequently hypercyclic polynomials of arbitrary positive degree. We also study distributional chaos for polynomials and show that every infinite-dimensional separable Banach space supports polynomials of arbitrary positive degree that have a dense distributionally scrambled linear manifold. © 2013 Nilson C. Bernardes Jr. and Alfredo Peris.The present work was done while the first author was visiting the Departament de Matematica Aplicada at Universitat Politecnica de Valencia (Spain). The first author is very grateful for the hospitality. The first author was supported in part by CAPES: Bolsista, Project no. BEX 4012/11-9. The second author was supported in part by MEC and FEDER, Project MTM2010-14909, and by GVA, Projects PROMETEO/2008/101 and PROMETEOII/2013/013.Hindawi Publishing CorporationDepartamento de Matemática AplicadaEscuela Técnica Superior de ArquitecturaInstituto Universitario de Matemática Pura y AplicadaCoordenaçao de Aperfeiçoamento de Pessoal de Nível Superior, BrasilGeneralitat ValencianaEuropean Regional Development FundMinisterio de Ciencia e InnovaciónRepositorio Institucional de la Universitat Politècnica de València Riunet20132013-01-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://riunet.upv.es/handle/10251/40690reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)InglésengGeneralitat Valenciana https://doi.org/10.13039/501100003359 PROMETEO08%2F2008%2F101 Análisis funcional, teoría de operadores y aplicacionesCoordenaçao de Aperfeiçoamento de Pessoal de Nível Superior, Brasil https://doi.org/10.13039/501100002322 BEX 4012%2F11-9Ministerio de Ciencia e Innovación http://dx.doi.org/10.13039/501100004837 MTM2010-14909 HIPERCICLICIDAD Y CAOS DE OPERADORESGeneralitat Valenciana https://doi.org/10.13039/501100003359 PROMETEOII%2F2013%2F013 Análisis funcional, teoría de operadores y sus aplicaciones (AFUNTOP)open accesshttp://purl.org/coar/access_right/c_abf2Reconocimiento (by)http://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/406902026-06-13T07:49:27Z
dc.title.none.fl_str_mv On the existence of polynomials with chaotic behaviour
title On the existence of polynomials with chaotic behaviour
spellingShingle On the existence of polynomials with chaotic behaviour
Bernardes, Nilson C.
Topological vector-spaces
Hypercyclic polynomials
Hypercyclic operators
Distributional chaos
Linear-operators
Banach-Spaces
Mixing polynomials
Frequently hypercyclic polynomials
Chaotic polynomials
MATEMATICA APLICADA
title_short On the existence of polynomials with chaotic behaviour
title_full On the existence of polynomials with chaotic behaviour
title_fullStr On the existence of polynomials with chaotic behaviour
title_full_unstemmed On the existence of polynomials with chaotic behaviour
title_sort On the existence of polynomials with chaotic behaviour
dc.creator.none.fl_str_mv Bernardes, Nilson C.
Peris Manguillot, Alfredo|||0000-0003-1683-2373
author Bernardes, Nilson C.
author_facet Bernardes, Nilson C.
Peris Manguillot, Alfredo|||0000-0003-1683-2373
author_role author
author2 Peris Manguillot, Alfredo|||0000-0003-1683-2373
author2_role author
dc.contributor.none.fl_str_mv Departamento de Matemática Aplicada
Escuela Técnica Superior de Arquitectura
Instituto Universitario de Matemática Pura y Aplicada
Coordenaçao de Aperfeiçoamento de Pessoal de Nível Superior, Brasil
Generalitat Valenciana
European Regional Development Fund
Ministerio de Ciencia e Innovación
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Topological vector-spaces
Hypercyclic polynomials
Hypercyclic operators
Distributional chaos
Linear-operators
Banach-Spaces
Mixing polynomials
Frequently hypercyclic polynomials
Chaotic polynomials
MATEMATICA APLICADA
topic Topological vector-spaces
Hypercyclic polynomials
Hypercyclic operators
Distributional chaos
Linear-operators
Banach-Spaces
Mixing polynomials
Frequently hypercyclic polynomials
Chaotic polynomials
MATEMATICA APLICADA
description We establish a general result on the existence of hypercyclic (resp., transitive, weakly mixing, mixing, frequently hypercyclic) polynomials on locally convex spaces. As a consequence we prove that every (real or complex) infinite-dimensional separable Frèchet space admits mixing (hence hypercyclic) polynomials of arbitrary positive degree. Moreover, every complex infinite-dimensional separable Banach space with an unconditional Schauder decomposition and every complex Frèchet space with an unconditional basis support chaotic and frequently hypercyclic polynomials of arbitrary positive degree. We also study distributional chaos for polynomials and show that every infinite-dimensional separable Banach space supports polynomials of arbitrary positive degree that have a dense distributionally scrambled linear manifold. © 2013 Nilson C. Bernardes Jr. and Alfredo Peris.
publishDate 2013
dc.date.none.fl_str_mv 2013
2013-01-01
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/10251/40690
url https://riunet.upv.es/handle/10251/40690
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Generalitat Valenciana https://doi.org/10.13039/501100003359 PROMETEO08%2F2008%2F101 Análisis funcional, teoría de operadores y aplicaciones
Coordenaçao de Aperfeiçoamento de Pessoal de Nível Superior, Brasil https://doi.org/10.13039/501100002322 BEX 4012%2F11-9
Ministerio de Ciencia e Innovación http://dx.doi.org/10.13039/501100004837 MTM2010-14909 HIPERCICLICIDAD Y CAOS DE OPERADORES
Generalitat Valenciana https://doi.org/10.13039/501100003359 PROMETEOII%2F2013%2F013 Análisis funcional, teoría de operadores y sus aplicaciones (AFUNTOP)
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reconocimiento (by)
http://creativecommons.org/licenses/by/4.0/
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
Reconocimiento (by)
http://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Hindawi Publishing Corporation
publisher.none.fl_str_mv Hindawi Publishing Corporation
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
_version_ 1869417084755116032
score 15.300724

Similares en LA Referencia