Piecewise smooth dynamical systems: Persistence of periodic solutions and normal forms
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Data
2016-04-05
Autores
Gouveia, Márcio R.A. [UNESP]
Llibre, Jaume
Novaes, Douglas D.
Pessoa, Claudio [UNESP]
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Resumo
We consider an n-dimensional piecewise smooth vector field with two zones separated by a hyperplane σ which admits an invariant hyperplane Ω transversal to σ 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.
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Crossing periodic solutions, Limit cycles, Lyapunov-Schmidt reduction, Normal forms, Piecewise differential system
Como citar
Journal of Differential Equations, v. 260, n. 7, p. 6108-6129, 2016.