Polynomial Differential Systems in R3 Having Invariant Weighted Homogeneous Surfaces
Autor(a) principal: | |
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Data de Publicação: | 2018 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1007/s00574-017-0045-9 http://hdl.handle.net/11449/174799 |
Resumo: | In 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. |
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Repositório Institucional da UNESP |
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Polynomial Differential Systems in R3 Having Invariant Weighted Homogeneous SurfacesDarboux theory of integrabilityInvariant algebraic surfacesPolynomial differential systemsSingular varietiesStratified vector fieldsVallis systemWeighted homogeneous surfacesIn 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.Departamento de Matemática e Computação Faculdade de Ciências e Tecnologia UNESP-Univ Estadual PaulistaDepartamento de Matemática Intituto de Biociências Letras e Ciências Exatas UNESP-Univ Estadual PaulistaDepartamento de Matemática e Computação Faculdade de Ciências e Tecnologia UNESP-Univ Estadual PaulistaDepartamento de Matemática Intituto de Biociências Letras e Ciências Exatas UNESP-Univ Estadual PaulistaUniversidade Estadual Paulista (Unesp)Dalbelo, Thaís Maria [UNESP]Messias, Marcelo [UNESP]Reinol, Alisson C. [UNESP]2018-12-11T17:12:55Z2018-12-11T17:12:55Z2018-03-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article137-157application/pdfhttp://dx.doi.org/10.1007/s00574-017-0045-9Bulletin of the Brazilian Mathematical Society, v. 49, n. 1, p. 137-157, 2018.1678-7544http://hdl.handle.net/11449/17479910.1007/s00574-017-0045-92-s2.0-850212738792-s2.0-85021273879.pdf3757225669056317Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengBulletin of the Brazilian Mathematical Society0,406info:eu-repo/semantics/openAccess2024-06-19T14:32:05Zoai:repositorio.unesp.br:11449/174799Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T19:57:34.782667Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Polynomial Differential Systems in R3 Having Invariant Weighted Homogeneous Surfaces |
title |
Polynomial Differential Systems in R3 Having Invariant Weighted Homogeneous Surfaces |
spellingShingle |
Polynomial Differential Systems in R3 Having Invariant Weighted Homogeneous Surfaces Dalbelo, Thaís Maria [UNESP] Darboux theory of integrability Invariant algebraic surfaces Polynomial differential systems Singular varieties Stratified vector fields Vallis system Weighted homogeneous surfaces |
title_short |
Polynomial Differential Systems in R3 Having Invariant Weighted Homogeneous Surfaces |
title_full |
Polynomial Differential Systems in R3 Having Invariant Weighted Homogeneous Surfaces |
title_fullStr |
Polynomial Differential Systems in R3 Having Invariant Weighted Homogeneous Surfaces |
title_full_unstemmed |
Polynomial Differential Systems in R3 Having Invariant Weighted Homogeneous Surfaces |
title_sort |
Polynomial Differential Systems in R3 Having Invariant Weighted Homogeneous Surfaces |
author |
Dalbelo, Thaís Maria [UNESP] |
author_facet |
Dalbelo, Thaís Maria [UNESP] 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 |
Universidade Estadual Paulista (Unesp) |
dc.contributor.author.fl_str_mv |
Dalbelo, Thaís Maria [UNESP] Messias, Marcelo [UNESP] Reinol, Alisson C. [UNESP] |
dc.subject.por.fl_str_mv |
Darboux theory of integrability Invariant algebraic surfaces Polynomial differential systems Singular varieties Stratified vector fields Vallis system Weighted homogeneous surfaces |
topic |
Darboux theory of integrability Invariant algebraic surfaces Polynomial differential systems Singular varieties Stratified vector fields Vallis system Weighted homogeneous surfaces |
description |
In 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. |
publishDate |
2018 |
dc.date.none.fl_str_mv |
2018-12-11T17:12:55Z 2018-12-11T17:12:55Z 2018-03-01 |
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/10.1007/s00574-017-0045-9 Bulletin of the Brazilian Mathematical Society, v. 49, n. 1, p. 137-157, 2018. 1678-7544 http://hdl.handle.net/11449/174799 10.1007/s00574-017-0045-9 2-s2.0-85021273879 2-s2.0-85021273879.pdf 3757225669056317 |
url |
http://dx.doi.org/10.1007/s00574-017-0045-9 http://hdl.handle.net/11449/174799 |
identifier_str_mv |
Bulletin of the Brazilian Mathematical Society, v. 49, n. 1, p. 137-157, 2018. 1678-7544 10.1007/s00574-017-0045-9 2-s2.0-85021273879 2-s2.0-85021273879.pdf 3757225669056317 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Bulletin of the Brazilian Mathematical Society 0,406 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
137-157 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_ |
1808129142607052800 |