Limit cycles and invariant cylinders for a class of continuous and discontinuous vector field in dimension 2n
Lima, Mauricio Firmino Silva (Universidade Federal do ABC(Brazil). Centro de Matematica Computacâo e Cognicâo)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2011
Abstract:	The subject of this paper concerns with the bifurcation of limit cycles and invariant cylinders from a global center of a linear differential system in dimension 2n perturbed inside a class of continuous and discontinuous piecewise linear differential systems. Our main results show that at most one limit cycle and at most one invariant cylinder can bifurcate using the expansion of the displacement function up to first order with respect to a small parameter. This upper bound is reached. For proving these results we use the averaging theory in a form where the differentiability of the system is not needed.
Grants:	Ministerio de Economía y Competitividad MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410
Note:	Agraïments: The first author is partially supported by CNPq grand number 200293/2010-9. Both authors are also supported by the joint project CAPES-MECD grant PHB-2009-0025-PC.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Equilibrium point ; Periodic orbit ; Limit cycle ; Invariant cylinder ; Continuous piecewise linear vector fields ; Discontinuous piecewise linear vector fields
Published in:	Applied Mathematics and Computation, Vol. 217 (2011) , p. 9985-9996, ISSN 1873-5649

DOI: 10.1016/j.amc.2011.04.069

Postprint 16 p, 374.4 KB

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