Expansivity and shadowing in linear dynamics
Autor(a) principal: | |
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Data de Publicação: | 2018 |
Outros Autores: | , , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1016/j.jmaa.2017.11.059 http://hdl.handle.net/11449/163907 |
Resumo: | In the early 1970's Eisenberg and Hedlund investigated relationships between expansivity and spectrum of operators on Banach spaces. In this paper we establish relationships between notions of expansivity and hypercyclicity, supercyclicity, Li-Yorke chaos and shadowing. In the case that the Banach space is c(0) or l(p) (1 <= p < infinity), we give complete characterizations of weighted shifts which satisfy various notions of expansivity. We also establish new relationships between notions of expansivity and spectrum. Moreover, we study various notions of shadowing for operators on Banach spaces. In particular, we solve a basic problem in linear dynamics by proving the existence of nonhyperbolic invertible operators with the shadowing property. This contrasts with the expected results for nonlinear dynamics on compact manifolds, illuminating the richness of dynamics of infinite dimensional linear operators. (C) 2017 Elsevier Inc. All rights reserved. |
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Expansivity and shadowing in linear dynamicsExpansiveHypercyclicLi-YorkeHyperbolicShadowingWeighted shiftsIn the early 1970's Eisenberg and Hedlund investigated relationships between expansivity and spectrum of operators on Banach spaces. In this paper we establish relationships between notions of expansivity and hypercyclicity, supercyclicity, Li-Yorke chaos and shadowing. In the case that the Banach space is c(0) or l(p) (1 <= p < infinity), we give complete characterizations of weighted shifts which satisfy various notions of expansivity. We also establish new relationships between notions of expansivity and spectrum. Moreover, we study various notions of shadowing for operators on Banach spaces. In particular, we solve a basic problem in linear dynamics by proving the existence of nonhyperbolic invertible operators with the shadowing property. This contrasts with the expected results for nonlinear dynamics on compact manifolds, illuminating the richness of dynamics of infinite dimensional linear operators. (C) 2017 Elsevier Inc. All rights reserved.Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Univ Fed Rio de Janeiro, Inst Matemat, Dept Matemat Aplicada, Caixa Postal 68530, BR-21945970 Rio De Janeiro, RJ, BrazilUniv Fed Sao Paulo, Inst Ciencia & Tecnol, Ave Cesare Mansueto Giulio Lattes 1201, BR-12247014 Sao Jose Dos Campos, SP, BrazilUniv Louisville, Dept Math, Louisville, KY 40292 USAAshoka Univ, Dept Math, Rajiv Gandhi Educ City K 131029, Rai, IndiaUniv Estadual Paulista, Dept Matemat, Rua Cristovao Colombo 2265, BR-15054000 Sao Jose Do Rio Preto, SP, BrazilInst Nacl Matemat Pura & Aplicada, Estr Dona Castorina 110, BR-22460320 Rio De Janeiro, RJ, BrazilUniv Estadual Paulista, Dept Matemat, Rua Cristovao Colombo 2265, BR-15054000 Sao Jose Do Rio Preto, SP, BrazilFAPESP: 2011/11663-5FAPESP: 2013/24541-0Elsevier B.V.Universidade Federal do Rio de Janeiro (UFRJ)Universidade Federal de São Paulo (UNIFESP)Univ LouisvilleAshoka UnivUniversidade Estadual Paulista (Unesp)Inst Nacl Matemat Pura & AplicadaBernardes, Nilson C.Cirilo, Patricia R.Darji, Udayan B.Messaoudi, Ali [UNESP]Pujals, Enrique R.2018-11-26T17:48:22Z2018-11-26T17:48:22Z2018-05-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article796-816application/pdfhttp://dx.doi.org/10.1016/j.jmaa.2017.11.059Journal Of Mathematical Analysis And Applications. San Diego: Academic Press Inc Elsevier Science, v. 461, n. 1, p. 796-816, 2018.0022-247Xhttp://hdl.handle.net/11449/16390710.1016/j.jmaa.2017.11.059WOS:000426141100044WOS000426141100044.pdfWeb of Sciencereponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengJournal Of Mathematical Analysis And Applicationsinfo:eu-repo/semantics/openAccess2023-11-18T06:17:24Zoai:repositorio.unesp.br:11449/163907Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462023-11-18T06:17:24Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Expansivity and shadowing in linear dynamics |
title |
Expansivity and shadowing in linear dynamics |
spellingShingle |
Expansivity and shadowing in linear dynamics Bernardes, Nilson C. Expansive Hypercyclic Li-Yorke Hyperbolic Shadowing Weighted shifts |
title_short |
Expansivity and shadowing in linear dynamics |
title_full |
Expansivity and shadowing in linear dynamics |
title_fullStr |
Expansivity and shadowing in linear dynamics |
title_full_unstemmed |
Expansivity and shadowing in linear dynamics |
title_sort |
Expansivity and shadowing in linear dynamics |
author |
Bernardes, Nilson C. |
author_facet |
Bernardes, Nilson C. Cirilo, Patricia R. Darji, Udayan B. Messaoudi, Ali [UNESP] Pujals, Enrique R. |
author_role |
author |
author2 |
Cirilo, Patricia R. Darji, Udayan B. Messaoudi, Ali [UNESP] Pujals, Enrique R. |
author2_role |
author author author author |
dc.contributor.none.fl_str_mv |
Universidade Federal do Rio de Janeiro (UFRJ) Universidade Federal de São Paulo (UNIFESP) Univ Louisville Ashoka Univ Universidade Estadual Paulista (Unesp) Inst Nacl Matemat Pura & Aplicada |
dc.contributor.author.fl_str_mv |
Bernardes, Nilson C. Cirilo, Patricia R. Darji, Udayan B. Messaoudi, Ali [UNESP] Pujals, Enrique R. |
dc.subject.por.fl_str_mv |
Expansive Hypercyclic Li-Yorke Hyperbolic Shadowing Weighted shifts |
topic |
Expansive Hypercyclic Li-Yorke Hyperbolic Shadowing Weighted shifts |
description |
In the early 1970's Eisenberg and Hedlund investigated relationships between expansivity and spectrum of operators on Banach spaces. In this paper we establish relationships between notions of expansivity and hypercyclicity, supercyclicity, Li-Yorke chaos and shadowing. In the case that the Banach space is c(0) or l(p) (1 <= p < infinity), we give complete characterizations of weighted shifts which satisfy various notions of expansivity. We also establish new relationships between notions of expansivity and spectrum. Moreover, we study various notions of shadowing for operators on Banach spaces. In particular, we solve a basic problem in linear dynamics by proving the existence of nonhyperbolic invertible operators with the shadowing property. This contrasts with the expected results for nonlinear dynamics on compact manifolds, illuminating the richness of dynamics of infinite dimensional linear operators. (C) 2017 Elsevier Inc. All rights reserved. |
publishDate |
2018 |
dc.date.none.fl_str_mv |
2018-11-26T17:48:22Z 2018-11-26T17:48:22Z 2018-05-01 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://dx.doi.org/10.1016/j.jmaa.2017.11.059 Journal Of Mathematical Analysis And Applications. San Diego: Academic Press Inc Elsevier Science, v. 461, n. 1, p. 796-816, 2018. 0022-247X http://hdl.handle.net/11449/163907 10.1016/j.jmaa.2017.11.059 WOS:000426141100044 WOS000426141100044.pdf |
url |
http://dx.doi.org/10.1016/j.jmaa.2017.11.059 http://hdl.handle.net/11449/163907 |
identifier_str_mv |
Journal Of Mathematical Analysis And Applications. San Diego: Academic Press Inc Elsevier Science, v. 461, n. 1, p. 796-816, 2018. 0022-247X 10.1016/j.jmaa.2017.11.059 WOS:000426141100044 WOS000426141100044.pdf |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Journal Of Mathematical Analysis And Applications |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
796-816 application/pdf |
dc.publisher.none.fl_str_mv |
Elsevier B.V. |
publisher.none.fl_str_mv |
Elsevier B.V. |
dc.source.none.fl_str_mv |
Web of Science reponame:Repositório Institucional da UNESP instname:Universidade Estadual Paulista (UNESP) instacron:UNESP |
instname_str |
Universidade Estadual Paulista (UNESP) |
instacron_str |
UNESP |
institution |
UNESP |
reponame_str |
Repositório Institucional da UNESP |
collection |
Repositório Institucional da UNESP |
repository.name.fl_str_mv |
Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP) |
repository.mail.fl_str_mv |
|
_version_ |
1803649751930896384 |