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

Bibliographic Details
Main Author: Buzzi, Claudio A. [UNESP]
Publication Date: 2024
Other Authors: Rodero, Ana Livia [UNESP], Torregrosa, Joan
Format: Article
Language: eng
Source: Repositório Institucional da UNESP
Download full: http://dx.doi.org/10.14232/ejqtde.2024.1.43
https://hdl.handle.net/11449/303585
Summary: 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.
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spelling 3-dimensional piecewise linear and quadratic vector fields with invariant spheres1-parameter families of closed trajectoriesinvariant conespiecewise smooth vector fields with invariant spheresWe 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.Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Agència de Gestió d'Ajuts Universitaris i de RecercaMinisterio de Ciencia, Innovación y UniversidadesUniversidade Estadual Paulista Instituto de Biociências Letras e Ciências Exatas, SPDepartamento de Matemática Instituto de Ciências Matemáticas e de Computação Universidade de São Paulo, Avenida Trabalhador São Carlense, 400, SPDepartament de Matemàtiques Universitat Autònoma de Barcelona, BarcelonaCentre de Recerca Matemàtica, Campus de Bellaterra, BarcelonaUniversidade Estadual Paulista Instituto de Biociências Letras e Ciências Exatas, SPCNPq: 2017/08779-8CNPq: 2019/00440-7CNPq: 2019/10269-3Agència de Gestió d'Ajuts Universitaris i de Recerca: 2021 SGR 00113CNPq: 2021/12630-5CNPq: 304798/2019-3Ministerio de Ciencia, Innovación y Universidades: PID2022-136613NB-I00Universidade Estadual Paulista (UNESP)Universidade de São Paulo (USP)Universitat Autònoma de BarcelonaCentre de Recerca MatemàticaBuzzi, Claudio A. [UNESP]Rodero, Ana Livia [UNESP]Torregrosa, Joan2025-04-29T19:30:05Z2024-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://dx.doi.org/10.14232/ejqtde.2024.1.43Electronic Journal of Qualitative Theory of Differential Equations, v. 2024, n. 43, 2024.1417-3875https://hdl.handle.net/11449/30358510.14232/ejqtde.2024.1.432-s2.0-85205451891Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengElectronic Journal of Qualitative Theory of Differential Equationsinfo:eu-repo/semantics/openAccess2025-04-30T14:09:13Zoai:repositorio.unesp.br:11449/303585Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestrepositoriounesp@unesp.bropendoar:29462025-04-30T14:09:13Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
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. [UNESP]
1-parameter families of closed trajectories
invariant cones
piecewise smooth vector fields with invariant spheres
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
author Buzzi, Claudio A. [UNESP]
author_facet Buzzi, Claudio A. [UNESP]
Rodero, Ana Livia [UNESP]
Torregrosa, Joan
author_role author
author2 Rodero, Ana Livia [UNESP]
Torregrosa, Joan
author2_role author
author
dc.contributor.none.fl_str_mv Universidade Estadual Paulista (UNESP)
Universidade de São Paulo (USP)
Universitat Autònoma de Barcelona
Centre de Recerca Matemàtica
dc.contributor.author.fl_str_mv Buzzi, Claudio A. [UNESP]
Rodero, Ana Livia [UNESP]
Torregrosa, Joan
dc.subject.por.fl_str_mv 1-parameter families of closed trajectories
invariant cones
piecewise smooth vector fields with invariant spheres
topic 1-parameter families of closed trajectories
invariant cones
piecewise smooth vector fields with invariant spheres
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 2024-01-01
2025-04-29T19:30:05Z
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/10.14232/ejqtde.2024.1.43
Electronic Journal of Qualitative Theory of Differential Equations, v. 2024, n. 43, 2024.
1417-3875
https://hdl.handle.net/11449/303585
10.14232/ejqtde.2024.1.43
2-s2.0-85205451891
url http://dx.doi.org/10.14232/ejqtde.2024.1.43
https://hdl.handle.net/11449/303585
identifier_str_mv Electronic Journal of Qualitative Theory of Differential Equations, v. 2024, n. 43, 2024.
1417-3875
10.14232/ejqtde.2024.1.43
2-s2.0-85205451891
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Electronic Journal of Qualitative Theory of Differential Equations
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.source.none.fl_str_mv Scopus
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 repositoriounesp@unesp.br
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