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Distributional chaos for operators on Banach spaces

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Distributional chaos for operators on Banach spaces

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dc.contributor.author Bernardes, Nilson C. es_ES
dc.contributor.author Bonilla, Antonio es_ES
dc.contributor.author Peris Manguillot, Alfredo es_ES
dc.contributor.author Wu, X. es_ES
dc.date.accessioned 2020-07-07T03:33:20Z
dc.date.available 2020-07-07T03:33:20Z
dc.date.issued 2018-03-15 es_ES
dc.identifier.issn 0022-247X es_ES
dc.identifier.uri http://hdl.handle.net/10251/147538
dc.description.abstract [EN] Four notions of distributional chaos, namely DC1, DC2, DC21/2 and DC3, are studied within the framework of operators on Banach spaces.. It is known that, for general dynamical systems, DC1 subset of DC2 subset of DC21/2 subset of DC3. We show that DC1 and DC2 coincide in our context, which answers a natural question. In contrast, there exist DC21/2 operators which are not DC2. Under the condition that there exists a dense set X-0 subset of X such that T(n)x -> 0 for any x is an element of X-0, DC3 operators are shown to be DC1. Moreover, we prove that any upper-frequently hypercyclic operator is DC21/2. Finally, several examples are provided to distinguish between different notions of distributional chaos, Li-Yorke chaos and irregularity. (C) 2017 Elsevier Inc. All rights reserved. es_ES
dc.description.sponsorship This work was partially done on a visit of the first author to the Departament de Matematica Aplicada at Universitat Politecnica de Valencia (Spain), and he is very grateful for the hospitality. The first author was supported by CNPq (Brazil) and by the EBW + Project (Erasmus Mundus Programme). The second and the third authors were supported by MINECO, Projects MTM2013-47093-P and MTM2016-75963-P, and by Generalitat Valenciana, Projects PROMETEOII/2013/013 and PROMETEO/2017/102. The fourth author was supported by the scientific research starting project of Southwest Petroleum University (No. 2015QHZ029) and the National Natural Science Foundation of China (No. 11601449). We thank the referee whose suggestions produced an improvement in the presentation of the paper. es_ES
dc.language Inglés es_ES
dc.publisher Elsevier es_ES
dc.relation.ispartof Journal of Mathematical Analysis and Applications es_ES
dc.rights Reconocimiento - No comercial - Sin obra derivada (by-nc-nd) es_ES
dc.subject Distributional chaos es_ES
dc.subject Hypercyclicity es_ES
dc.subject Upper-frequent hypercyclicity es_ES
dc.subject Distributionally irregular vector es_ES
dc.subject Absolutely mean irregular vector es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title Distributional chaos for operators on Banach spaces es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.1016/j.jmaa.2017.11.005 es_ES
dc.relation.projectID info:eu-repo/grantAgreement/NSFC//11601449/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/SWPU//2015QHZ029/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/GVA//PROMETEOII%2F2013%2F013/ES/Análisis funcional, teoría de operadores y sus aplicaciones (AFUNTOP)/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/MINECO//MTM2013-47093-P/ES/HIPERCICLICIDAD Y CAOS DE OPERADORES/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/MINECO//MTM2016-75963-P/ES/DINAMICA DE OPERADORES/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/GVA//PROMETEO%2F2017%2F102/ES/ANALISIS FUNCIONAL, TEORIA DE OPERADORES Y APLICACIONES/ es_ES
dc.rights.accessRights Abierto es_ES
dc.contributor.affiliation Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada es_ES
dc.description.bibliographicCitation Bernardes, NC.; Bonilla, A.; Peris Manguillot, A.; Wu, X. (2018). Distributional chaos for operators on Banach spaces. Journal of Mathematical Analysis and Applications. 459(2):797-821. https://doi.org/10.1016/j.jmaa.2017.11.005 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion https://doi.org/10.1016/j.jmaa.2017.11.005 es_ES
dc.description.upvformatpinicio 797 es_ES
dc.description.upvformatpfin 821 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 459 es_ES
dc.description.issue 2 es_ES
dc.relation.pasarela S\384323 es_ES
dc.contributor.funder Generalitat Valenciana es_ES
dc.contributor.funder Southwest Petroleum University es_ES
dc.contributor.funder National Natural Science Foundation of China es_ES
dc.contributor.funder Conselho Nacional de Desenvolvimento Científico e Tecnológico, Brasil es_ES
dc.contributor.funder Ministerio de Economía y Competitividad es_ES


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