Abstract

In this talk we deal with a 4-dimensional family of periodic linear systems depending on three parameters $\lambda$₁, $\lambda$₂, $\epsilon$. The stability parameters for $\epsilon =0$ are easily obtained due to the fact that in this case we obtain a constant coefficients system. We use the normal form technique to study the stability parameters for $\epsilon >0$ and small enough.

As an application we study the stability parameters for the homographic solutions of a planar three body problem for some homogeneous potentials and, in particular, for the Newtonian case.