Periodic orbits near equilibria via averaging theory of second order
Barreira, Luis (Instituto Superior Técnico(Portugal). Departamento de Matemática)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Valls, Clàudia 1973- (Instituto Superior Técnico(Portugal). Departamento de Matemática)

Date:	2012
Abstract:	Lyapunov, Weinstein and Moser obtained remarkable theorems giving sufficient conditions for the existence of periodic orbits emanating from an equilibrium point of a differential system with a first integral. Using averaging theory of first order we established in [1] a similar result for a differential system without assuming the existence of a first integral. Now, using averaging theory of second order, we extend our result to the case when the first order average is identically zero. Our result can be interpreted as a kind of special Hopf bifurcation.
Grants:	Ministerio de Ciencia e Innovación MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410
Note:	Agraïments: The first and third authors were partially supported by FCT through CAMGSD, Lisbon.
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Document:	Article
Subject:	Periodic orbit ; Averaging theory of second order ; Hopf bifurcation
Published in:	Mathematical Modelling and Analysis, Vol. 17 Núm. 5 (2012), p. 715-731, ISSN 1648-3510

Postprint 17 p, 323.7 KB

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