STABLE PIECEWISE POLYNOMIAL VECTOR FIELDS

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dc.contributor.authorPessoa, Claudio [UNESP]
dc.contributor.authorSotomayor, Jorge
dc.contributor.institutionUniversidade Estadual Paulista (Unesp)
dc.contributor.institutionUniversidade de São Paulo (USP)
dc.date.accessioned2014-05-20T14:02:56Z
dc.date.available2014-05-20T14:02:56Z
dc.date.issued2012-09-22
dc.description.abstractLet N = {y > 0} and S = {y < 0} be the semi-planes of R-2 having as common boundary the line D = {y = 0}. Let X and Y be polynomial vector fields defined in N and S, respectively, leading to a discontinuous piecewise polynomial vector field Z = (X, Y). This work pursues the stability and the transition analysis of solutions of Z between N and S, started by Filippov (1988) and Kozlova (1984) and reformulated by Sotomayor-Teixeira (1995) in terms of the regularization method. This method consists in analyzing a one parameter family of continuous vector fields Z(epsilon), defined by averaging X and Y. This family approaches Z when the parameter goes to zero. The results of Sotomayor-Teixeira and Sotomayor-Machado (2002) providing conditions on (X, Y) for the regularized vector fields to be structurally stable on planar compact connected regions are extended to discontinuous piecewise polynomial vector fields on R-2. Pertinent genericity results for vector fields satisfying the above stability conditions are also extended to the present case. A procedure for the study of discontinuous piecewise vector fields at infinity through a compactification is proposed here.en
dc.description.affiliationUniv Estadual Paulista, UNESP IBILCE, BR-15054000 Sao Jose do Rio Preto, SP, Brazil
dc.description.affiliationUniv São Paulo, Inst Matemat & Estat, BR-05508090 São Paulo, Brazil
dc.description.affiliationUnespUniv Estadual Paulista, UNESP IBILCE, BR-15054000 Sao Jose do Rio Preto, SP, Brazil
dc.description.sponsorshipFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
dc.description.sponsorshipPró-Reitoria de Pesquisa da UNESP (PROPe UNESP)
dc.description.sponsorshipIdFAPESP: 11/13152-8
dc.format.extent15
dc.identifierhttp://ejde.math.txstate.edu/
dc.identifier.citationElectronic Journal of Differential Equations. San Marcos: Texas State Univ, p. 15, 2012.
dc.identifier.fileWOS000310454000002.pdf
dc.identifier.issn1072-6691
dc.identifier.lattes3724937886557424
dc.identifier.orcid0000-0001-6790-1055
dc.identifier.urihttp://hdl.handle.net/11449/22171
dc.identifier.wosWOS:000310454000002
dc.language.isoeng
dc.publisherTexas State Univ
dc.relation.ispartofElectronic Journal of Differential Equations
dc.relation.ispartofjcr0.944
dc.relation.ispartofsjr0,538
dc.rights.accessRightsAcesso aberto
dc.sourceWeb of Science
dc.subjectStructural stabilityen
dc.subjectpiecewise vector fieldsen
dc.subjectcompactification.en
dc.titleSTABLE PIECEWISE POLYNOMIAL VECTOR FIELDSen
dc.typeArtigo
dcterms.licensehttp://ejde.math.txstate.edu/i2authors.html
dcterms.rightsHolderTexas State Univ
unesp.author.lattes3724937886557424[1]
unesp.author.orcid0000-0001-6790-1055[1]

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