Negatively Invariant Sets and Entire Trajectories of Set-Valued Dynamical Systems

Strongly negatively invariant compact sets of set-valued autonomous and nonautonomous dynamical systems on a complete metric space, the latter formulated in terms of processes, are shown to contain a weakly positively invariant family and hence entire solutions. For completeness the strongly positiv...

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Detalles Bibliográficos
Autores: Kloeden, Peter E., Marín Rubio, Pedro
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2011
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/25934
Acceso en línea:http://hdl.handle.net/11441/25934
https://doi.org/10.1007/s11228-009-0123-2
Access Level:acceso abierto
Palabra clave:Entire solutions
Invariant sets
Positively invariant sets
Negatively invariant sets
Set-valued dynamical systems
Autonomous and nonautonomous dynamical systems
Set-valued processes
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spelling Negatively Invariant Sets and Entire Trajectories of Set-Valued Dynamical SystemsKloeden, Peter E.Marín Rubio, PedroEntire solutionsInvariant setsPositively invariant setsNegatively invariant setsSet-valued dynamical systemsAutonomous and nonautonomous dynamical systemsSet-valued processesStrongly negatively invariant compact sets of set-valued autonomous and nonautonomous dynamical systems on a complete metric space, the latter formulated in terms of processes, are shown to contain a weakly positively invariant family and hence entire solutions. For completeness the strongly positively invariant case is also considered, where the obtained invariant family is strongly invariant. Both discrete and continuous time systems are treated. In the nonautonomous case, the various types of invariant families are in fact composed of subsets of the state space that are mapped onto each other by the set-valued process. A simple example shows the usefulness of the result for showing the occurrence of a bifurcation in a set-valued dynamical system.Springer Verlag (Germany)Ecuaciones Diferenciales y Análisis Numérico2011info:eu-repo/semantics/articleinfo:eu-repo/semantics/submittedVersionapplication/pdfapplication/pdfhttp://hdl.handle.net/11441/25934https://doi.org/10.1007/s11228-009-0123-2reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésJournal of Dynamics and Differential Equations, 19 (1), 437-450http://doi.org/10.1007/s11228-009-0123-2info:eu-repo/semantics/openAccessoai:idus.us.es:11441/259342026-06-17T12:51:07Z
dc.title.none.fl_str_mv Negatively Invariant Sets and Entire Trajectories of Set-Valued Dynamical Systems
title Negatively Invariant Sets and Entire Trajectories of Set-Valued Dynamical Systems
spellingShingle Negatively Invariant Sets and Entire Trajectories of Set-Valued Dynamical Systems
Kloeden, Peter E.
Entire solutions
Invariant sets
Positively invariant sets
Negatively invariant sets
Set-valued dynamical systems
Autonomous and nonautonomous dynamical systems
Set-valued processes
title_short Negatively Invariant Sets and Entire Trajectories of Set-Valued Dynamical Systems
title_full Negatively Invariant Sets and Entire Trajectories of Set-Valued Dynamical Systems
title_fullStr Negatively Invariant Sets and Entire Trajectories of Set-Valued Dynamical Systems
title_full_unstemmed Negatively Invariant Sets and Entire Trajectories of Set-Valued Dynamical Systems
title_sort Negatively Invariant Sets and Entire Trajectories of Set-Valued Dynamical Systems
dc.creator.none.fl_str_mv Kloeden, Peter E.
Marín Rubio, Pedro
author Kloeden, Peter E.
author_facet Kloeden, Peter E.
Marín Rubio, Pedro
author_role author
author2 Marín Rubio, Pedro
author2_role author
dc.contributor.none.fl_str_mv Ecuaciones Diferenciales y Análisis Numérico
dc.subject.none.fl_str_mv Entire solutions
Invariant sets
Positively invariant sets
Negatively invariant sets
Set-valued dynamical systems
Autonomous and nonautonomous dynamical systems
Set-valued processes
topic Entire solutions
Invariant sets
Positively invariant sets
Negatively invariant sets
Set-valued dynamical systems
Autonomous and nonautonomous dynamical systems
Set-valued processes
description Strongly negatively invariant compact sets of set-valued autonomous and nonautonomous dynamical systems on a complete metric space, the latter formulated in terms of processes, are shown to contain a weakly positively invariant family and hence entire solutions. For completeness the strongly positively invariant case is also considered, where the obtained invariant family is strongly invariant. Both discrete and continuous time systems are treated. In the nonautonomous case, the various types of invariant families are in fact composed of subsets of the state space that are mapped onto each other by the set-valued process. A simple example shows the usefulness of the result for showing the occurrence of a bifurcation in a set-valued dynamical system.
publishDate 2011
dc.date.none.fl_str_mv 2011
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 http://hdl.handle.net/11441/25934
https://doi.org/10.1007/s11228-009-0123-2
url http://hdl.handle.net/11441/25934
https://doi.org/10.1007/s11228-009-0123-2
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Journal of Dynamics and Differential Equations, 19 (1), 437-450
http://doi.org/10.1007/s11228-009-0123-2
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 Springer Verlag (Germany)
publisher.none.fl_str_mv Springer Verlag (Germany)
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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