Bifurcation of Limit cycles from a 4-dimensional center in R^m in resonance 1:N
Barreira, Luis (Universidade Técnica de Lisboa. Departamento de Matemática)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Valls, Clàudia 1973- (Universidade Técnica de Lisboa. Departamento de Matemática)

Date:	2012
Abstract:	For every positive integer N ≥ 2 we consider the linear differential center ˙x = Ax in Rm with eigenvalues ±i, ±N i and 0 with multiplicity m − 4. We perturb this linear center inside the class of all polynomial differential systems of the form linear plus a homogeneous nonlinearity of degree N, i. e. x˙ = Ax + εF(x) where every component of F(x) is a linear polynomial plus a homogeneous polynomial of degree N. When the displacement function of order ε of the perturbed system is not identically zero, we study the maximal number of limit cycles that can bifurcate from the periodic orbits of the linear differential center. In particular, we give explicit upper bounds for the number of limit cycles.
Grants:	Ministerio de Ciencia y Tecnología MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410
Note:	Agraïments: The first and third authors are partially supported by FCT through CAMGSD, Lisbon.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Periodic orbit ; Averaging theory ; Limit cycles ; Resonance 1 : N
Published in:	Journal of mathematical analysis and applications, Vol. 389 (2012) , p. 754-768, ISSN 1096-0813

DOI: 10.1016/j.jmaa.2011.12.018

Postprint 18 p, 730.8 KB

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