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Piecewise linear perturbations of a linear center
Buzzi, Claudio (Universidade Estadual Paulista(Brazil). Departamento de Matemática)
Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Pessoa, Claudio (Universidade Estadual Paulista(Brazil). Departamento de Matemática)

Fecha: 2013
Resumen: This paper is mainly devoted to study the limit cycles that can bifurcate from a linear center using a piecewise linear perturbation in two zones. We consider the case when the two zones are separated by a straight line Σ and the singular point of the unperturbed system is in Σ. It is proved that the maximum number of limit cycles that can appear up to a seventh order perturbation is three. Moreover this upper bound is reached. This result confirm that these systems have more limit cycles than it was expected. Finally, center and isochronicity problems are also studied in systems which include a first order perturbation. For these last systems it is also proved that, when the period function, defined in the period annulus of the center, is not monotone, then it has at most one critical period. Moreover this upper bound is also reached.
Nota: Agraïments: The first author is supported by FAPESP-BRAZIL grant 2007/06896-5 and CAPES-PROCAD-BRAZIL grant 035/2007. The second author is supported by FAPESP-Brazil Project 2011/13152-8 and by Programa Primeiros Projetos-PROPe/UNESP. The first and the third authors are also supported by the joint project CAPES-MECD grant PHB-2009-0025-PC
Nota: Número d'acord de subvenció MICINN/MTM2008-03437
Nota: Número d'acord de subvenció AGAUR/2009/SGR-410
Derechos: Tots els drets reservats.
Lengua: Anglès
Documento: article ; recerca ; acceptedVersion
Materia: Non-smooth differential system ; Limit cycle ; Piecewise linear differential system
Publicado en: Discrete and continuous dynamical systems. Series A, Vol. 33 Núm. 9 (2013) , p. 3915-3936, ISSN 1553-5231

DOI: 10.3934/dcds.2013.33.3915

18 p, 411.1 KB

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