Stable piecewise polynomial vector fields

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MetadadosDescriçãoIdioma
Autor(es): dc.contributorUniversidade Estadual Paulista (UNESP)-
Autor(es): dc.contributorUniversidade de São Paulo (USP)-
Autor(es): dc.creatorPessoa, Claudio [UNESP]-
Autor(es): dc.creatorSotomayor, Jorge-
Data de aceite: dc.date.accessioned2022-08-04T22:02:56Z-
Data de disponibilização: dc.date.available2022-08-04T22:02:56Z-
Data de envio: dc.date.issued2022-04-28-
Data de envio: dc.date.issued2022-04-28-
Data de envio: dc.date.issued2012-09-22-
Fonte completa do material: dc.identifierhttp://hdl.handle.net/11449/219840-
Fonte: dc.identifier.urihttp://educapes.capes.gov.br/handle/11449/219840-
Descrição: dc.descriptionLet 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 ∈, 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. © 2012 Texas State University - San Marcos.-
Descrição: dc.descriptionUniversidade Estadual Paulista UNESP-IBILCE, Av. Cristovão Colombo, 2265, 15.054-000, S. J. Rio Preto, SP-
Descrição: dc.descriptionInstituto de Matemática e Estatística Universidade de São Paulo, Rua do Matão 1010, Cidade Universitaria, 05.508-090, São Paulo, SP-
Descrição: dc.descriptionUniversidade Estadual Paulista UNESP-IBILCE, Av. Cristovão Colombo, 2265, 15.054-000, S. J. Rio Preto, SP-
Idioma: dc.languageen-
Relação: dc.relationElectronic Journal of Differential Equations-
???dc.source???: dc.sourceScopus-
Palavras-chave: dc.subjectCompactification-
Palavras-chave: dc.subjectPiecewise vector fields-
Palavras-chave: dc.subjectStructural stability-
Título: dc.titleStable piecewise polynomial vector fields-
Tipo de arquivo: dc.typelivro digital-
Aparece nas coleções:Repositório Institucional - Unesp

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