GLOBAL DYNAMICS of THE LORENZ SYSTEM WITH INVARIANT ALGEBRAIC SURFACES

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dc.contributor.authorLlibre, Jaume
dc.contributor.authorMessias, Marcelo [UNESP]
dc.contributor.authorDa Silva, Paulo Ricardo [UNESP]
dc.contributor.institutionUniv Autonoma Barcelona
dc.contributor.institutionUniversidade Estadual Paulista (Unesp)
dc.date.accessioned2014-05-20T13:23:33Z
dc.date.available2014-05-20T13:23:33Z
dc.date.issued2010-10-01
dc.description.abstractIn this paper by using the Poincare compactification of R(3) we describe the global dynamics of the Lorenz system(x) over dot = s(-x + y), (y) over dot = rx - y - xz, (z) over dot = -bz + xy,having some invariant algebraic surfaces. of course ( x, y, z) is an element of R(3) are the state variables and (s, r, b) is an element of R(3) are the parameters. For six sets of the parameter values, the Lorenz system has invariant algebraic surfaces. For these six sets, we provide the global phase portrait of the system in the Poincare ball (i.e. in the compactification of R(3) with the sphere S(2) of the infinity).en
dc.description.affiliationUniv Autonoma Barcelona, Dept Matemat, Barcelona 08193, Catalonia, Spain
dc.description.affiliationUniv Estadual Paulista, UNESP, Fac Ciencias & Tecnol, Dept Matemat Estat & Comp, BR-19060900 São Paulo, Brazil
dc.description.affiliationUniv Estadual Paulista, UNESP, Inst Biociencias Letras & Ciencias Exatas, Dept Matemat, BR-15054000 São Paulo, Brazil
dc.description.affiliationUnespUniv Estadual Paulista, UNESP, Fac Ciencias & Tecnol, Dept Matemat Estat & Comp, BR-19060900 São Paulo, Brazil
dc.description.affiliationUnespUniv Estadual Paulista, UNESP, Inst Biociencias Letras & Ciencias Exatas, Dept Matemat, BR-15054000 São Paulo, Brazil
dc.description.sponsorshipCICYT
dc.description.sponsorshipConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
dc.description.sponsorshipCoordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
dc.description.sponsorshipFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
dc.description.sponsorshipIdCICYT: 2009SGR 410
dc.description.sponsorshipIdCNPq: 305204/2009-2
dc.description.sponsorshipIdMTM2008-03437
dc.format.extent3137-3155
dc.identifierhttp://dx.doi.org/10.1142/S0218127410027593
dc.identifier.citationInternational Journal of Bifurcation and Chaos. Singapore: World Scientific Publ Co Pte Ltd, v. 20, n. 10, p. 3137-3155, 2010.
dc.identifier.doi10.1142/S0218127410027593
dc.identifier.issn0218-1274
dc.identifier.lattes3757225669056317
dc.identifier.lattes6050955861168161
dc.identifier.orcid0000-0002-1430-5986
dc.identifier.urihttp://hdl.handle.net/11449/7118
dc.identifier.wosWOS:000286430000006
dc.language.isoeng
dc.publisherWorld Scientific Publ Co Pte Ltd
dc.relation.ispartofInternational Journal of Bifurcation and Chaos
dc.relation.ispartofjcr1.501
dc.relation.ispartofsjr0,568
dc.rights.accessRightsAcesso restrito
dc.sourceWeb of Science
dc.subjectIntegrabilityen
dc.subjectLorenz systemen
dc.subjectPoincare compactificationen
dc.subjectdynamics at infinity invariant algebraic surfaceen
dc.titleGLOBAL DYNAMICS of THE LORENZ SYSTEM WITH INVARIANT ALGEBRAIC SURFACESen
dc.typeArtigo
dcterms.licensehttp://www.worldscientific.com/page/authors/author-rights
dcterms.rightsHolderWorld Scientific Publ Co Pte Ltd
unesp.author.lattes3757225669056317
unesp.author.lattes6050955861168161[3]
unesp.author.orcid0000-0002-9511-5999[1]
unesp.author.orcid0000-0002-1430-5986[3]
unesp.author.orcid0000-0003-2269-7091[2]
unesp.campusUniversidade Estadual Paulista (Unesp), Faculdade de Ciências e Tecnologia, Presidente Prudentept

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