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Finite Intersection Property and Dynamical Compactness

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Finite Intersection Property and Dynamical Compactness

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dc.contributor.author Huang, Wen es_ES
dc.contributor.author Khilko, Danylo es_ES
dc.contributor.author Kolyada, Sergey es_ES
dc.contributor.author Peris Manguillot, Alfredo es_ES
dc.contributor.author Zhang, Guohua es_ES
dc.date.accessioned 2020-07-04T03:31:41Z
dc.date.available 2020-07-04T03:31:41Z
dc.date.issued 2018-09 es_ES
dc.identifier.issn 1040-7294 es_ES
dc.identifier.uri http://hdl.handle.net/10251/147417
dc.description.abstract [EN] Dynamical compactness with respect to a family as a new concept of chaoticity of a dynamical system was introduced and discussed in Huang et al. (J Differ Equ 260(9):6800-6827, 2016). In this paper we continue to investigate this notion. In particular, we prove that all dynamical systems are dynamically compact with respect to a Furstenberg family if and only if this family has the finite intersection property. We investigate weak mixing and weak disjointness by using the concept of dynamical compactness. We also explore further difference between transitive compactness and weak mixing. As a byproduct, we show that the -limit and the -limit sets of a point may have quite different topological structure. Moreover, the equivalence between multi-sensitivity, sensitive compactness and transitive sensitivity is established for a minimal system. Finally, these notions are also explored in the context of linear dynamics. es_ES
dc.description.sponsorship Wen Huang and Sergii Kolyada acknowledge the hospitality of the School of Mathematical Sciences of the Fudan University, Shanghai. Sergii Kolyada also acknowledges the hospitality of the Max-Planck-Institute fur Mathematik (MPIM) in Bonn, the Departament de Matematica Aplicada of the Universitat Politecnica de Valencia, the partial support of Project MTM2013-47093-P, and the Department of Mathematics of the Chinese University of Hong Kong. We thank the referees for careful reading and constructive comments that have resulted in substantial improvements to this paper. Wen Huang was supported by NNSF of China (11225105, 11431012); Alfred Peris was supported by MINECO, Projects MTM2013-47093-P and MTM2016-75963-P, and by GVA, Project PROMETEOII/2013/013; and Guohua Zhang was supported by NNSF of China (11671094). es_ES
dc.language Inglés es_ES
dc.publisher Springer-Verlag es_ES
dc.relation.ispartof Journal of Dynamics and Differential Equations es_ES
dc.rights Reserva de todos los derechos es_ES
dc.subject Dynamical topology es_ES
dc.subject Dynamical compactness es_ES
dc.subject Transitive compactness es_ES
dc.subject Sensitive compactness es_ES
dc.subject Topological weak mixing es_ES
dc.subject Multi-sensitivity es_ES
dc.subject Transitive sensitivity es_ES
dc.subject Linear dynamics es_ES
dc.subject Hypercyclic operator es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title Finite Intersection Property and Dynamical Compactness es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.1007/s10884-017-9600-8 es_ES
dc.relation.projectID info:eu-repo/grantAgreement/NSFC//11225105/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/NSFC//11431012/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/NSFC//11671094/ 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 Huang, W.; Khilko, D.; Kolyada, S.; Peris Manguillot, A.; Zhang, G. (2018). Finite Intersection Property and Dynamical Compactness. Journal of Dynamics and Differential Equations. 30(3):1221-1245. https://doi.org/10.1007/s10884-017-9600-8 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion https://doi.org/10.1007/s10884-017-9600-8 es_ES
dc.description.upvformatpinicio 1221 es_ES
dc.description.upvformatpfin 1245 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 30 es_ES
dc.description.issue 3 es_ES
dc.relation.pasarela S\384322 es_ES
dc.contributor.funder Generalitat Valenciana es_ES
dc.contributor.funder National Natural Science Foundation of China es_ES
dc.contributor.funder Ministerio de Economía y Competitividad es_ES
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