Estabilidad no lineal de sub-armonicos en el problema de tres cuerpos de sitnikov.

Since the 60s have been published many papers on the dynamics of a restricted 3-body problem known as the problem of Sitnikov, where eccentricity e∈ [0.1 [of elliptic orbits describing the primaries bodies acting as parameter. In the last two decades some authors have found a variety of global families of periodic and symmetric orbits, "branches arcwised-connected" that arise in this model, either for bifurcating from the equilibrium located in the center of mass of the system for certain values positive eccentricity or from certain periodic orbits of the circular case (e = 0), obtaining enough information of its oscillatory properties. The results of the seed capital project PUJ Cali, "global Continuation of regular and stability in a restricted 3-body problem solutions", which we developed in 2014, show that the two branches of 2π-periodic solutions emerging of the circular problem are linearly stable for larger eccentricities 0.5. although this fact was confirmed numerically, the effective range of linear stability (ie, analytically proved) is much lower order. It wants to investigate first whether this property holds for all branches 2Nπ-periodic (sub-harmonics) problem bifurcating of circular problem when N> 2 and second, study their nonlinear stability when N = 1. The methodology consists of a quantified adaptation of the method of Poincare then combined with the Twist Moser theorem.