Normal forms and global phase portraits of quadratic and cubic integrable vector fields having two nonconcentric circles as invariant algebraic curves

Detalhes bibliográficos
Autor(a) principal: Llibre, Jaume
Data de Publicação: 2017
Outros Autores: Messias, Marcelo [UNESP], Reinol, Alisson C. [UNESP]
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.1080/14689367.2016.1263600
http://hdl.handle.net/11449/173924
Resumo: In this paper, we give the normal form of all planar polynomial vector fields of degree d ≤ 3 having two nonconcentric circles C1 and C2 as invariant algebraic curves and the function H=Cβ 1 Cα 2, with α and β real values, as first integral. Moreover, we classify all global phase portraits on the Poincaré disc of a subclass of these vector fields.
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spelling Normal forms and global phase portraits of quadratic and cubic integrable vector fields having two nonconcentric circles as invariant algebraic curvesglobal analysisinvariant algebraic curveslimit cyclesnormal formsPoincaré compactificationQuadratic and cubic vector fieldsIn this paper, we give the normal form of all planar polynomial vector fields of degree d ≤ 3 having two nonconcentric circles C1 and C2 as invariant algebraic curves and the function H=Cβ 1 Cα 2, with α and β real values, as first integral. Moreover, we classify all global phase portraits on the Poincaré disc of a subclass of these vector fields.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Agència de Gestió d’Ajuts Universitaris i de RecercaConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Institució Catalana de Recerca i Estudis AvançatsCoordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Ministerio de Economía y CompetitividadDepartament de Matemàtiques Universitat Autònoma de BarcelonaDepartamento de Matemática e Computação Faculdade de Ciências e Tecnologia Universidade Estadual Paulista UNESPDepartamento de Matemática e Computação Faculdade de Ciências e Tecnologia Universidade Estadual Paulista UNESPFAPESP: 2013/24541-0FAPESP: 2013/26602-7Agència de Gestió d’Ajuts Universitaris i de Recerca: 2013SGR--568FAPESP: 2016/01258-0CNPq: 308159/2015-2Institució Catalana de Recerca i Estudis Avançats: 316338CAPES: 88881.030454/2013--01Institució Catalana de Recerca i Estudis Avançats: FEDER--UNAB10--4E--378Institució Catalana de Recerca i Estudis Avançats: FP7--PEOPLE--2012--IRSES 318999Ministerio de Economía y Competitividad: MTM2008--03437Ministerio de Economía y Competitividad: MTM2013--40998--PUniversitat Autònoma de BarcelonaUniversidade Estadual Paulista (Unesp)Llibre, JaumeMessias, Marcelo [UNESP]Reinol, Alisson C. [UNESP]2018-12-11T17:08:22Z2018-12-11T17:08:22Z2017-07-03info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article374-390application/pdfhttp://dx.doi.org/10.1080/14689367.2016.1263600Dynamical Systems, v. 32, n. 3, p. 374-390, 2017.1468-93751468-9367http://hdl.handle.net/11449/17392410.1080/14689367.2016.12636002-s2.0-850061411872-s2.0-85006141187.pdf3757225669056317Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengDynamical Systems0,295info:eu-repo/semantics/openAccess2024-06-19T14:32:05Zoai:repositorio.unesp.br:11449/173924Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T19:20:38.634034Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Normal forms and global phase portraits of quadratic and cubic integrable vector fields having two nonconcentric circles as invariant algebraic curves
title Normal forms and global phase portraits of quadratic and cubic integrable vector fields having two nonconcentric circles as invariant algebraic curves
spellingShingle Normal forms and global phase portraits of quadratic and cubic integrable vector fields having two nonconcentric circles as invariant algebraic curves
Llibre, Jaume
global analysis
invariant algebraic curves
limit cycles
normal forms
Poincaré compactification
Quadratic and cubic vector fields
title_short Normal forms and global phase portraits of quadratic and cubic integrable vector fields having two nonconcentric circles as invariant algebraic curves
title_full Normal forms and global phase portraits of quadratic and cubic integrable vector fields having two nonconcentric circles as invariant algebraic curves
title_fullStr Normal forms and global phase portraits of quadratic and cubic integrable vector fields having two nonconcentric circles as invariant algebraic curves
title_full_unstemmed Normal forms and global phase portraits of quadratic and cubic integrable vector fields having two nonconcentric circles as invariant algebraic curves
title_sort Normal forms and global phase portraits of quadratic and cubic integrable vector fields having two nonconcentric circles as invariant algebraic curves
author Llibre, Jaume
author_facet Llibre, Jaume
Messias, Marcelo [UNESP]
Reinol, Alisson C. [UNESP]
author_role author
author2 Messias, Marcelo [UNESP]
Reinol, Alisson C. [UNESP]
author2_role author
author
dc.contributor.none.fl_str_mv Universitat Autònoma de Barcelona
Universidade Estadual Paulista (Unesp)
dc.contributor.author.fl_str_mv Llibre, Jaume
Messias, Marcelo [UNESP]
Reinol, Alisson C. [UNESP]
dc.subject.por.fl_str_mv global analysis
invariant algebraic curves
limit cycles
normal forms
Poincaré compactification
Quadratic and cubic vector fields
topic global analysis
invariant algebraic curves
limit cycles
normal forms
Poincaré compactification
Quadratic and cubic vector fields
description In this paper, we give the normal form of all planar polynomial vector fields of degree d ≤ 3 having two nonconcentric circles C1 and C2 as invariant algebraic curves and the function H=Cβ 1 Cα 2, with α and β real values, as first integral. Moreover, we classify all global phase portraits on the Poincaré disc of a subclass of these vector fields.
publishDate 2017
dc.date.none.fl_str_mv 2017-07-03
2018-12-11T17:08:22Z
2018-12-11T17:08:22Z
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/10.1080/14689367.2016.1263600
Dynamical Systems, v. 32, n. 3, p. 374-390, 2017.
1468-9375
1468-9367
http://hdl.handle.net/11449/173924
10.1080/14689367.2016.1263600
2-s2.0-85006141187
2-s2.0-85006141187.pdf
3757225669056317
url http://dx.doi.org/10.1080/14689367.2016.1263600
http://hdl.handle.net/11449/173924
identifier_str_mv Dynamical Systems, v. 32, n. 3, p. 374-390, 2017.
1468-9375
1468-9367
10.1080/14689367.2016.1263600
2-s2.0-85006141187
2-s2.0-85006141187.pdf
3757225669056317
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Dynamical Systems
0,295
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 374-390
application/pdf
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
_version_ 1808129055268012032

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