On set-valued discrete dynamical systems

In this paper, we attempt to study set-valued discrete dynamical systems with the objective of developing a general framework and unifying some results and definitions in the literature. For these purposes, we follow similar ideas to those existing for classical dynamical systems. We focus on discre...

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Detalles Bibliográficos
Autores: Hernández García, Elvira, Perán Mazón, Juan Jacobo
Tipo de recurso: artículo
Fecha de publicación:2023
País:España
Institución:Universidad Nacional de Educación a Distancia
Repositorio:e-spacio. Repositorio Institucional de la UNED
Idioma:inglés
OAI Identifier:oai:e-spacio.uned.es:20.500.14468/26921
Acceso en línea:https://hdl.handle.net/20.500.14468/26921
Access Level:acceso abierto
Palabra clave:1299 Otras especialidades matemáticas
Discrete-time
limit sets
Lyapunov Stability
Set-valued dynamical systems
Set-valued maps.
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spelling On set-valued discrete dynamical systemsHernández García, ElviraPerán Mazón, Juan Jacobo1299 Otras especialidades matemáticasDiscrete-timelimit setsLyapunov StabilitySet-valued dynamical systemsSet-valued maps.In this paper, we attempt to study set-valued discrete dynamical systems with the objective of developing a general framework and unifying some results and definitions in the literature. For these purposes, we follow similar ideas to those existing for classical dynamical systems. We focus on discrete dynamical systems in terms of set-valued maps. The solutions associated to our systems are given by sequences of sets. We obtain preliminary results by formulating appropriate notions of set dynamical systems as attractor, stability and invariant sets. For this purpose, we study the ω-limit sets which play an important role for gaining an overall understanding of how the system is behaving, particularly in the long term. We study its properties by using well-known notions from set-valued analysis. We are able to generalize dynamical results in terms of single valued maps by the weaker assumptions on continuity.Biemdas Academic Publisherse-Spacio UNED20252025-06-2520232023-10-0120232023-10-01journal articlehttp://purl.org/coar/resource_type/c_6501info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/20.500.14468/26921reponame:e-spacio. Repositorio Institucional de la UNEDinstname:Universidad Nacional de Educación a DistanciaInglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-nd/4.0/deed.esoai:e-spacio.uned.es:20.500.14468/269212026-06-06T12:38:31Z
dc.title.none.fl_str_mv On set-valued discrete dynamical systems
title On set-valued discrete dynamical systems
spellingShingle On set-valued discrete dynamical systems
Hernández García, Elvira
1299 Otras especialidades matemáticas
Discrete-time
limit sets
Lyapunov Stability
Set-valued dynamical systems
Set-valued maps.
title_short On set-valued discrete dynamical systems
title_full On set-valued discrete dynamical systems
title_fullStr On set-valued discrete dynamical systems
title_full_unstemmed On set-valued discrete dynamical systems
title_sort On set-valued discrete dynamical systems
dc.creator.none.fl_str_mv Hernández García, Elvira
Perán Mazón, Juan Jacobo
author Hernández García, Elvira
author_facet Hernández García, Elvira
Perán Mazón, Juan Jacobo
author_role author
author2 Perán Mazón, Juan Jacobo
author2_role author
dc.contributor.none.fl_str_mv e-Spacio UNED
dc.subject.none.fl_str_mv 1299 Otras especialidades matemáticas
Discrete-time
limit sets
Lyapunov Stability
Set-valued dynamical systems
Set-valued maps.
topic 1299 Otras especialidades matemáticas
Discrete-time
limit sets
Lyapunov Stability
Set-valued dynamical systems
Set-valued maps.
description In this paper, we attempt to study set-valued discrete dynamical systems with the objective of developing a general framework and unifying some results and definitions in the literature. For these purposes, we follow similar ideas to those existing for classical dynamical systems. We focus on discrete dynamical systems in terms of set-valued maps. The solutions associated to our systems are given by sequences of sets. We obtain preliminary results by formulating appropriate notions of set dynamical systems as attractor, stability and invariant sets. For this purpose, we study the ω-limit sets which play an important role for gaining an overall understanding of how the system is behaving, particularly in the long term. We study its properties by using well-known notions from set-valued analysis. We are able to generalize dynamical results in terms of single valued maps by the weaker assumptions on continuity.
publishDate 2023
dc.date.none.fl_str_mv 2023
2023-10-01
2023
2023-10-01
2025
2025-06-25
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/20.500.14468/26921
url https://hdl.handle.net/20.500.14468/26921
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by-nc-nd/4.0/deed.es
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
http://creativecommons.org/licenses/by-nc-nd/4.0/deed.es
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Biemdas Academic Publishers
publisher.none.fl_str_mv Biemdas Academic Publishers
dc.source.none.fl_str_mv reponame:e-spacio. Repositorio Institucional de la UNED
instname:Universidad Nacional de Educación a Distancia
instname_str Universidad Nacional de Educación a Distancia
reponame_str e-spacio. Repositorio Institucional de la UNED
collection e-spacio. Repositorio Institucional de la UNED
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.812429

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