Topological properties of prolongations and stable sets for semigroup actions

Detalhes bibliográficos
Autor(a) principal: Rocha, Victor H. L. [UNESP]
Data de Publicação: 2021
Outros Autores: Reis, Ronan A. [UNESP]
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.1016/j.topol.2021.107611
http://hdl.handle.net/11449/210077
Resumo: In this paper we study topological properties of Lyapunov stable sets for semigroup actions on Tychonoff spaces. We show that the stability and the asymptotical stability of a compact set is characterized by the stability and the asymptotical stability of its components, respectively. We also present a characterization of the stability of a compact set by means of omega-limit sets, prolongations, prolongational limit sets and the existence of a fundamental system of invariant neighborhoods of it. (c) 2021 Elsevier B.V. All rights reserved.
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spelling Topological properties of prolongations and stable sets for semigroup actionsLyapunov stabilityAsymptotical stabilityConnected componentsProlongationsSemigroup actionsIn this paper we study topological properties of Lyapunov stable sets for semigroup actions on Tychonoff spaces. We show that the stability and the asymptotical stability of a compact set is characterized by the stability and the asymptotical stability of its components, respectively. We also present a characterization of the stability of a compact set by means of omega-limit sets, prolongations, prolongational limit sets and the existence of a fundamental system of invariant neighborhoods of it. (c) 2021 Elsevier B.V. All rights reserved.Univ Estadual Paulista, Dept Matemat & Comp, R Roberto Simonsen 305, BR-19060080 Presidente Prudente, SP, BrazilUniv Estadual Paulista, Dept Matemat & Comp, R Roberto Simonsen 305, BR-19060080 Presidente Prudente, SP, BrazilElsevier B.V.Universidade Estadual Paulista (Unesp)Rocha, Victor H. L. [UNESP]Reis, Ronan A. [UNESP]2021-06-25T12:39:00Z2021-06-25T12:39:00Z2021-03-15info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article22http://dx.doi.org/10.1016/j.topol.2021.107611Topology And Its Applications. Amsterdam: Elsevier, v. 291, 22 p., 2021.0166-8641http://hdl.handle.net/11449/21007710.1016/j.topol.2021.107611WOS:000623100400006Web of Sciencereponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengTopology And Its Applicationsinfo:eu-repo/semantics/openAccess2024-06-19T14:31:50Zoai:repositorio.unesp.br:11449/210077Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T14:55:54.956406Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Topological properties of prolongations and stable sets for semigroup actions
title Topological properties of prolongations and stable sets for semigroup actions
spellingShingle Topological properties of prolongations and stable sets for semigroup actions
Rocha, Victor H. L. [UNESP]
Lyapunov stability
Asymptotical stability
Connected components
Prolongations
Semigroup actions
title_short Topological properties of prolongations and stable sets for semigroup actions
title_full Topological properties of prolongations and stable sets for semigroup actions
title_fullStr Topological properties of prolongations and stable sets for semigroup actions
title_full_unstemmed Topological properties of prolongations and stable sets for semigroup actions
title_sort Topological properties of prolongations and stable sets for semigroup actions
author Rocha, Victor H. L. [UNESP]
author_facet Rocha, Victor H. L. [UNESP]
Reis, Ronan A. [UNESP]
author_role author
author2 Reis, Ronan A. [UNESP]
author2_role author
dc.contributor.none.fl_str_mv Universidade Estadual Paulista (Unesp)
dc.contributor.author.fl_str_mv Rocha, Victor H. L. [UNESP]
Reis, Ronan A. [UNESP]
dc.subject.por.fl_str_mv Lyapunov stability
Asymptotical stability
Connected components
Prolongations
Semigroup actions
topic Lyapunov stability
Asymptotical stability
Connected components
Prolongations
Semigroup actions
description In this paper we study topological properties of Lyapunov stable sets for semigroup actions on Tychonoff spaces. We show that the stability and the asymptotical stability of a compact set is characterized by the stability and the asymptotical stability of its components, respectively. We also present a characterization of the stability of a compact set by means of omega-limit sets, prolongations, prolongational limit sets and the existence of a fundamental system of invariant neighborhoods of it. (c) 2021 Elsevier B.V. All rights reserved.
publishDate 2021
dc.date.none.fl_str_mv 2021-06-25T12:39:00Z
2021-06-25T12:39:00Z
2021-03-15
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.topol.2021.107611
Topology And Its Applications. Amsterdam: Elsevier, v. 291, 22 p., 2021.
0166-8641
http://hdl.handle.net/11449/210077
10.1016/j.topol.2021.107611
WOS:000623100400006
url http://dx.doi.org/10.1016/j.topol.2021.107611
http://hdl.handle.net/11449/210077
identifier_str_mv Topology And Its Applications. Amsterdam: Elsevier, v. 291, 22 p., 2021.
0166-8641
10.1016/j.topol.2021.107611
WOS:000623100400006
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Topology And Its Applications
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 22
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_ 1808128437158674432

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