Morse decomposition for gradient-like multi-valued autonomous and nonautonomous dynamical systems

In this paper, we first prove that the property of being a gradientlike general dynamical system and the existence of a Morse decomposition are equivalent. Next, the stability of gradient-like general dynamical systems is analyzed. In particular, we show that a gradient-like general dynamical system...

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Detalhes bibliográficos
Autores: Wang, Yejuan, Caraballo Garrido, Tomás
Formato: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2020
País:España
Recursos:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/100790
Acesso em linha:https://hdl.handle.net/11441/100790
https://doi.org/10.3934/dcdss.2020092
Access Level:acceso abierto
Palavra-chave:Gradient-like general dynamical systems
Morse decomposition
Nonautonomous multi-valued dynamical systems
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spelling Morse decomposition for gradient-like multi-valued autonomous and nonautonomous dynamical systemsWang, YejuanCaraballo Garrido, TomásGradient-like general dynamical systemsMorse decompositionNonautonomous multi-valued dynamical systemsIn this paper, we first prove that the property of being a gradientlike general dynamical system and the existence of a Morse decomposition are equivalent. Next, the stability of gradient-like general dynamical systems is analyzed. In particular, we show that a gradient-like general dynamical system is stable under perturbations, and that Morse sets are upper semicontinuous with respect to perturbations. Moreover, we prove that any solution of perturbed general dynamical systems should be close to some Morse set of the unperturbed gradient-like general dynamical system. We do not assume local compactness for the metric phase space X, unlike previous results in the literature. Finally, we extend the Morse decomposition theory of single-valued nonautonomous dynamical systems to the multi-valued case, without imposing any compactness of the parameter spaces.American Institute of Mathematical Sciences (AIMS)Ecuaciones Diferenciales y Análisis NuméricoFQM314: Análisis Estocástico de Sistemas DiferencialesNational Natural Science Foundation of ChinaFundamental Research Funds for the Central UniversitiesMinisterio de Economía y Competitividad (MINECO). EspañaEuropean Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER)Junta de Andalucía. Consejería de Innovación Ciencia y Empresa2020info:eu-repo/semantics/articleinfo:eu-repo/semantics/submittedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/100790https://doi.org/10.3934/dcdss.2020092reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésDiscrete and Continuous Dynamical Systems - Series S, 13 (8), 2303-2326.4187508411571153lzujbky-2018-it58lzujbky-2018-ot03MTM2015-63723-PP12-FQM-1492https://www.aimsciences.org/article/doi/10.3934/dcdss.2020092info:eu-repo/semantics/openAccessoai:idus.us.es:11441/1007902026-06-17T12:51:07Z
dc.title.none.fl_str_mv Morse decomposition for gradient-like multi-valued autonomous and nonautonomous dynamical systems
title Morse decomposition for gradient-like multi-valued autonomous and nonautonomous dynamical systems
spellingShingle Morse decomposition for gradient-like multi-valued autonomous and nonautonomous dynamical systems
Wang, Yejuan
Gradient-like general dynamical systems
Morse decomposition
Nonautonomous multi-valued dynamical systems
title_short Morse decomposition for gradient-like multi-valued autonomous and nonautonomous dynamical systems
title_full Morse decomposition for gradient-like multi-valued autonomous and nonautonomous dynamical systems
title_fullStr Morse decomposition for gradient-like multi-valued autonomous and nonautonomous dynamical systems
title_full_unstemmed Morse decomposition for gradient-like multi-valued autonomous and nonautonomous dynamical systems
title_sort Morse decomposition for gradient-like multi-valued autonomous and nonautonomous dynamical systems
dc.creator.none.fl_str_mv Wang, Yejuan
Caraballo Garrido, Tomás
author Wang, Yejuan
author_facet Wang, Yejuan
Caraballo Garrido, Tomás
author_role author
author2 Caraballo Garrido, Tomás
author2_role author
dc.contributor.none.fl_str_mv Ecuaciones Diferenciales y Análisis Numérico
FQM314: Análisis Estocástico de Sistemas Diferenciales
National Natural Science Foundation of China
Fundamental Research Funds for the Central Universities
Ministerio de Economía y Competitividad (MINECO). España
European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER)
Junta de Andalucía. Consejería de Innovación Ciencia y Empresa
dc.subject.none.fl_str_mv Gradient-like general dynamical systems
Morse decomposition
Nonautonomous multi-valued dynamical systems
topic Gradient-like general dynamical systems
Morse decomposition
Nonautonomous multi-valued dynamical systems
description In this paper, we first prove that the property of being a gradientlike general dynamical system and the existence of a Morse decomposition are equivalent. Next, the stability of gradient-like general dynamical systems is analyzed. In particular, we show that a gradient-like general dynamical system is stable under perturbations, and that Morse sets are upper semicontinuous with respect to perturbations. Moreover, we prove that any solution of perturbed general dynamical systems should be close to some Morse set of the unperturbed gradient-like general dynamical system. We do not assume local compactness for the metric phase space X, unlike previous results in the literature. Finally, we extend the Morse decomposition theory of single-valued nonautonomous dynamical systems to the multi-valued case, without imposing any compactness of the parameter spaces.
publishDate 2020
dc.date.none.fl_str_mv 2020
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/submittedVersion
format article
status_str submittedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/100790
https://doi.org/10.3934/dcdss.2020092
url https://hdl.handle.net/11441/100790
https://doi.org/10.3934/dcdss.2020092
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Discrete and Continuous Dynamical Systems - Series S, 13 (8), 2303-2326.
41875084
11571153
lzujbky-2018-it58
lzujbky-2018-ot03
MTM2015-63723-P
P12-FQM-1492
https://www.aimsciences.org/article/doi/10.3934/dcdss.2020092
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv American Institute of Mathematical Sciences (AIMS)
publisher.none.fl_str_mv American Institute of Mathematical Sciences (AIMS)
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300719

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