Piecewise smooth dynamical systems: Persistence of periodic solutions and normal forms
Gouveia, Márcio (Ibilce - UNESP (Brasil). Departamento de Matemática)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Novaes, Douglas D. (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Pessoa, Claudio (Ibilce - UNESP (Brasil). Departamento de Matemática)

Date:	2016
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.
Grants:	Ministerio de Economía y Competitividad MTM2013-40998-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-568 European Commission 316338 European Commission 316339
Note:	Agraïments: The first and fourth author are partially supported by a FAPESP grant 2013/34541-0. The first and fourth authors are supported by a CAPES PROCAD grant 88881.068462/2014-01. The second author is partially supported by a CAPES CSF-PVE grant 88881.030454/ 2013-01. The third author is supported by a FAPESP grant 2015/02517-6.
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Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Crossing periodic orbits ; Limit cycle ; Lyapunov-Schmidt reduction ; Piecewise differential system
Published in:	Journal of differential equations, Vol. 260 (2016) , p. 6108-6129, ISSN 1090-2732

DOI: 10.1016/j.jde.2015.12.034

Postprint 23 p, 542.3 KB

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Research literature > UAB research groups literature > Research Centres and Groups (research output) > Experimental sciences > GSD (Dynamical systems)
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