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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

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

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Author(s):
Gouveia, Marcio R. A. [1] ; Llibre, Jaume [2] ; Novaes, Douglas D. [3] ; Pessoa, Claudio [1]
Total Authors: 4
Affiliation:
[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
Total Affiliations: 3
Document type: Journal article
Source: Journal of Differential Equations; v. 260, n. 7, p. 6108-6129, APR 5 2016.
Web of Science Citations: 1
Abstract

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)

FAPESP's process: 15/02517-6 - Study of minimal sets in nonsmooth dynamical systems
Grantee:Douglas Duarte Novaes
Support Opportunities: Scholarships in Brazil - Post-Doctoral