Periodic orbits near equilibria via averaging theory of second order

    Luis Barreira Affiliation
    ; Jaume Llibre Affiliation
    ; Claudia Valls Affiliation


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 the 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 degenerated Hopf bifurcation.

Keyword : differential equation, nonlinear differential equation, perturbation method

How to Cite
Barreira, L., Llibre, J., & Valls, C. (2012). Periodic orbits near equilibria via averaging theory of second order. Mathematical Modelling and Analysis, 17(5), 715-731.
Published in Issue
Nov 1, 2012
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