Abstract

The talk deals with the period function of quadratic centers. In the literature it is used different terminology to classify these centers, but essentially there are four families: Hamiltonian, reversible, codimension four and generalized Lotka-Volterra systems. Chicone has conjectured that the reversible centers have at most two critical periods, and that the centers of the three other families have a monotonic period function. With regard to the second part of this conjecture, until now it has been proved the monotonicity in the Hamiltonian and codimension four families. In this talk we shall prove some partial results for the generalized Lotka-Volterra systems.