Polynomial Differential Systems in R3 Having Invariant Weighted Homogeneous Surfaces

dc.contributor.authorDalbelo, Thaís Maria [UNESP]
dc.contributor.authorMessias, Marcelo [UNESP]
dc.contributor.authorReinol, Alisson C. [UNESP]
dc.contributor.institutionUniversidade Estadual Paulista (Unesp)
dc.date.accessioned2018-12-11T17:12:55Z
dc.date.available2018-12-11T17:12:55Z
dc.date.issued2018-03-01
dc.description.abstractIn this paper we give the normal form of all polynomial differential systems in R3 having a weighted homogeneous surface f= 0 as an invariant algebraic surface and characterize among these systems those having a Darboux invariant constructed uniquely using this invariant surface. Using the obtained results we give some examples of stratified vector fields, when f= 0 is a singular surface. We also apply the obtained results to study the Vallis system, which is related to the so-called El Niño atmospheric phenomenon, when it has a cone as an invariant algebraic surface, performing a dynamical analysis of the flow of this system restricted to the invariant cone and providing a stratification for this singular surface.en
dc.description.affiliationDepartamento de Matemática e Computação Faculdade de Ciências e Tecnologia UNESP-Univ Estadual Paulista
dc.description.affiliationDepartamento de Matemática Intituto de Biociências Letras e Ciências Exatas UNESP-Univ Estadual Paulista
dc.description.affiliationUnespDepartamento de Matemática e Computação Faculdade de Ciências e Tecnologia UNESP-Univ Estadual Paulista
dc.description.affiliationUnespDepartamento de Matemática Intituto de Biociências Letras e Ciências Exatas UNESP-Univ Estadual Paulista
dc.format.extent137-157
dc.identifierhttp://dx.doi.org/10.1007/s00574-017-0045-9
dc.identifier.citationBulletin of the Brazilian Mathematical Society, v. 49, n. 1, p. 137-157, 2018.
dc.identifier.doi10.1007/s00574-017-0045-9
dc.identifier.file2-s2.0-85021273879.pdf
dc.identifier.issn1678-7544
dc.identifier.lattes3757225669056317
dc.identifier.scopus2-s2.0-85021273879
dc.identifier.urihttp://hdl.handle.net/11449/174799
dc.language.isoeng
dc.relation.ispartofBulletin of the Brazilian Mathematical Society
dc.relation.ispartofsjr0,406
dc.rights.accessRightsAcesso aberto
dc.sourceScopus
dc.subjectDarboux theory of integrability
dc.subjectInvariant algebraic surfaces
dc.subjectPolynomial differential systems
dc.subjectSingular varieties
dc.subjectStratified vector fields
dc.subjectVallis system
dc.subjectWeighted homogeneous surfaces
dc.titlePolynomial Differential Systems in R3 Having Invariant Weighted Homogeneous Surfacesen
dc.typeArtigo
unesp.author.lattes3757225669056317
unesp.departmentMatemática e Computação - FCTpt

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