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| Home > Articles > Published articles > Piecewise smooth dynamical systems: Persistence of periodic solutions and normal forms |
(IBILCE-UNESP(Brazil). Departamento de Matemática) (Universitat Autònoma de Barcelona. Departament de Matemàtiques) (Universitat Autònoma de Barcelona. Departament de Matemàtiques)| 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. |
| 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. |
| Note: | Número d'acord de subvenció MINECO/MTM2013-40998-P |
| Note: | Número d'acord de subvenció AGAUR/2014/SGR-568 |
| Note: | Número d'acord de subvenció EC/FP7/2012/316338 |
| Note: | Número d'acord de subvenció EC/FP7/2012/316339 |
| Rights: | Tots els drets reservats.  |
| Language: | Anglès |
| Document: | article ; recerca ; acceptedVersion |
| 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 |
23 p, 542.3 KB |
