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On the existence of polynomials with chaotic behaviour

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On the existence of polynomials with chaotic behaviour

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dc.contributor.author Bernardes, Nilson C. es_ES
dc.contributor.author Peris Manguillot, Alfredo es_ES
dc.date.accessioned 2014-10-07T08:32:11Z
dc.date.available 2014-10-07T08:32:11Z
dc.date.issued 2013
dc.identifier.issn 0972-6802
dc.identifier.uri http://hdl.handle.net/10251/40690
dc.description.abstract 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. es_ES
dc.description.sponsorship 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. en_EN
dc.language Inglés es_ES
dc.publisher Hindawi Publishing Corporation es_ES
dc.relation.ispartof Journal of Function Spaces and Applications es_ES
dc.rights Reconocimiento (by) es_ES
dc.subject Topological vector-spaces es_ES
dc.subject Hypercyclic polynomials es_ES
dc.subject Hypercyclic operators es_ES
dc.subject Distributional chaos es_ES
dc.subject Linear-operators es_ES
dc.subject Banach-Spaces es_ES
dc.subject Mixing polynomials es_ES
dc.subject Frequently hypercyclic polynomials es_ES
dc.subject Chaotic polynomials es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title On the existence of polynomials with chaotic behaviour es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.1155/2013/320961
dc.relation.projectID info:eu-repo/grantAgreement/GVA//PROMETEO08%2F2008%2F101/ES/Análisis funcional, teoría de operadores y aplicaciones/
dc.relation.projectID info:eu-repo/grantAgreement/CAPES//BEX 4012%2F11-9/
dc.relation.projectID info:eu-repo/grantAgreement/MICINN//MTM2010-14909/ES/HIPERCICLICIDAD Y CAOS DE OPERADORES/
dc.relation.projectID info:eu-repo/grantAgreement/GVA//PROMETEOII%2F2013%2F013/ES/Análisis funcional, teoría de operadores y sus aplicaciones (AFUNTOP)/
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.; Peris Manguillot, A. (2013). On the existence of polynomials with chaotic behaviour. Journal of Function Spaces and Applications. 2013(320961). https://doi.org/10.1155/2013/320961 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion http://dx.doi.org/10.1155/2013/320961 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 2013 es_ES
dc.description.issue 320961 es_ES
dc.relation.senia 259506
dc.identifier.eissn 1758-4965
dc.contributor.funder Coordenaçao de Aperfeiçoamento de Pessoal de Nível Superior, Brasil
dc.contributor.funder Generalitat Valenciana
dc.contributor.funder European Regional Development Fund
dc.contributor.funder Ministerio de Ciencia e Innovación es_ES
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