Regularization of discontinuous foliations: Blowing up and sliding conditions via Fenichel theory

Autor(es)

Panazzolo, Daniel ^{[1, 2]} ; da Silva, Paulo R. ^[3]

Afiliação do(s) autor(es)

^[1] UHA, Lab Mathemat Informat & Applicat, 4 Rue Freres Lumiere, F-68093 Mulhouse - France

^[2] Univ Strasbourg, Strasbourg - France

^[3] Univ Estadual Paulista, IBILCE, Dept Matemat, Rua C Colombo, 2265, BR-15054000 Sao Paulo - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Journal of Differential Equations; v. 263, n. 12, p. 8362-8390, DEC 15 2017.
• Citações Web of Science: 3

Resumo

We study the regularization of an oriented 1-foliation F on M \textbackslash{} Sigma where M is a smooth manifold and Sigma subset of M is a closed subset, which can be interpreted as the discontinuity locus of F. In the spirit of Filippov's work, we define a sliding and sewing dynamics on the discontinuity locus Sigma as some sort of limit of the dynamics of a nearby smooth 1-foliation and obtain conditions to identify whether a point belongs to the sliding or sewing regions. (C) 2017 Elsevier Inc. All rights reserved. (AU)

• Processo FAPESP: 13/24541-0 - Teorias ergódica e qualitativa dos sistemas dinâmicos
• Beneficiário: Claudio Aguinaldo Buzzi
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 16/02031-9 - Regularização de variedades folheadas descontinuamente
• Beneficiário: Paulo Ricardo da Silva
• Modalidade de apoio: Auxílio à Pesquisa - Pesquisador Visitante - Internacional