3-dimensional piecewise linear and quadratic vector fields with invariant spheres

We consider the class X of 3-dimensional piecewise smooth vector fields that admit a first integral which leaves invariant any sphere centered at the origin. In this class, we prove that a linear vector field does not admit isolated invariant cones. Moreover, we provide the existence of at least ten...

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Autores: Buzzi, Claudio A., Rodero, Ana Livia|||0000-0002-6595-1881, Torregrosa, Joan|||0000-0002-2753-1827
Tipo de recurso: artículo
Fecha de publicación:2024
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:303170
Acceso en línea:https://ddd.uab.cat/record/303170
https://dx.doi.org/urn:doi:10.14232/ejqtde.2024.1.43
Access Level:acceso abierto
Palabra clave:Piecewise smooth vector fields with invariant spheres
Invariant cones
1-parameter families of closed trajectories
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spelling 3-dimensional piecewise linear and quadratic vector fields with invariant spheresBuzzi, Claudio A.Rodero, Ana Livia|||0000-0002-6595-1881Torregrosa, Joan|||0000-0002-2753-1827Piecewise smooth vector fields with invariant spheresInvariant cones1-parameter families of closed trajectoriesWe consider the class X of 3-dimensional piecewise smooth vector fields that admit a first integral which leaves invariant any sphere centered at the origin. In this class, we prove that a linear vector field does not admit isolated invariant cones. Moreover, we provide the existence of at least ten 1-parameter families of crossing closed trajectories for quadratic vector fields in X. 22024-01-0120242024-01-01Articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/303170https://dx.doi.org/urn:doi:10.14232/ejqtde.2024.1.43reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengAgència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2021/SGR-00113Agencia Estatal de Investigación https://doi.org/10.13039/501100011033 PID2022-136613NB-I00Agencia Estatal de Investigación https://doi.org/10.13039/501100011033 CEX2020-001084-MEuropean Commission https://doi.org/10.13039/501100000780 777911open accesshttp://purl.org/coar/access_right/c_abf2Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, la comunicació pública de l'obra i la creació d'obres derivades, fins i tot amb finalitats comercials, sempre i quan es reconegui l'autoria de l'obra original.https://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:ddd.uab.cat:3031702026-06-06T12:50:31Z
dc.title.none.fl_str_mv 3-dimensional piecewise linear and quadratic vector fields with invariant spheres
title 3-dimensional piecewise linear and quadratic vector fields with invariant spheres
spellingShingle 3-dimensional piecewise linear and quadratic vector fields with invariant spheres
Buzzi, Claudio A.
Piecewise smooth vector fields with invariant spheres
Invariant cones
1-parameter families of closed trajectories
title_short 3-dimensional piecewise linear and quadratic vector fields with invariant spheres
title_full 3-dimensional piecewise linear and quadratic vector fields with invariant spheres
title_fullStr 3-dimensional piecewise linear and quadratic vector fields with invariant spheres
title_full_unstemmed 3-dimensional piecewise linear and quadratic vector fields with invariant spheres
title_sort 3-dimensional piecewise linear and quadratic vector fields with invariant spheres
dc.creator.none.fl_str_mv Buzzi, Claudio A.
Rodero, Ana Livia|||0000-0002-6595-1881
Torregrosa, Joan|||0000-0002-2753-1827
author Buzzi, Claudio A.
author_facet Buzzi, Claudio A.
Rodero, Ana Livia|||0000-0002-6595-1881
Torregrosa, Joan|||0000-0002-2753-1827
author_role author
author2 Rodero, Ana Livia|||0000-0002-6595-1881
Torregrosa, Joan|||0000-0002-2753-1827
author2_role author
author
dc.subject.none.fl_str_mv Piecewise smooth vector fields with invariant spheres
Invariant cones
1-parameter families of closed trajectories
topic Piecewise smooth vector fields with invariant spheres
Invariant cones
1-parameter families of closed trajectories
description We consider the class X of 3-dimensional piecewise smooth vector fields that admit a first integral which leaves invariant any sphere centered at the origin. In this class, we prove that a linear vector field does not admit isolated invariant cones. Moreover, we provide the existence of at least ten 1-parameter families of crossing closed trajectories for quadratic vector fields in X.
publishDate 2024
dc.date.none.fl_str_mv 2
2024-01-01
2024
2024-01-01
dc.type.none.fl_str_mv Article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://ddd.uab.cat/record/303170
https://dx.doi.org/urn:doi:10.14232/ejqtde.2024.1.43
url https://ddd.uab.cat/record/303170
https://dx.doi.org/urn:doi:10.14232/ejqtde.2024.1.43
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2021/SGR-00113
Agencia Estatal de Investigación https://doi.org/10.13039/501100011033 PID2022-136613NB-I00
Agencia Estatal de Investigación https://doi.org/10.13039/501100011033 CEX2020-001084-M
European Commission https://doi.org/10.13039/501100000780 777911
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://creativecommons.org/licenses/by/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Dipòsit Digital de Documents de la UAB
instname:Universitat Autònoma de Barcelona
instname_str Universitat Autònoma de Barcelona
reponame_str Dipòsit Digital de Documents de la UAB
collection Dipòsit Digital de Documents de la UAB
repository.name.fl_str_mv
repository.mail.fl_str_mv
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