Piecewise smooth dynamical systems: Persistence of periodic solutions and normal forms

Autor(es)

Gouveia, Marcio R. A. ^[1] ; Llibre, Jaume ^[2] ; Novaes, Douglas D. ^[3] ; Pessoa, Claudio ^[1]

Afiliação do(s) autor(es)

^[1] IBILCE UNESP, Dept Matemat, Rua C Colombo 2265, BR-15054000 S J Rio Preto, SP - Brazil

^[2] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Catalonia - Spain

^[3] Univ Estadual Campinas, Dept Matemat, Rua Sergio Baruque de Holanda 651, BR-13083859 Campinas, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Journal of Differential Equations; v. 260, n. 7, p. 6108-6129, APR 5 2016.
• Citações Web of Science: 1

Resumo

We consider an n-dimensional piecewise smooth vector field with two zones separated by a hyperplane Sigma which admits an invariant hyperplane Omega transversal to Sigma containing a period annulus A fulfilled by crossing periodic solutions. For small discontinuous perturbations of these systems we develop a Melnikov-like function to control the persistence of periodic solutions contained in A. When n = 3 we provide normal forms for the piecewise linear case. Finally we apply the Melnikov-like function to study discontinuous perturbations of the given normal forms. (C) 2015 Elsevier Inc. All rights reserved. (AU)

• Processo FAPESP: 15/02517-6 - Estudo de conjuntos minimais em sistemas dinâmicos não suaves
• Beneficiário: Douglas Duarte Novaes
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado