Continuacion global de soluciones periodicas y estabilidad en un problema restringido de 3 cuerpos.

From the sixties many works has been published about the dynamics in a special 3-body problem known as the Sitnikov problem, where the eccentricity of primaries e∈[0,1[ acts as a parameter. In the last two decades some authors have found several global families of symmetric periodic solutions (“arcwise connected branches”) arising in this model by bifurcating either from the equilibrium at the center of mass at certain positive values of the eccentricity or from any periodic orbit in the circular problem (e=0) being well understood theirs oscillatory properties. These families may change its stability character for some values of e. actually little it is known about the stability properties of them. We investigate the linear stability of some them in order to estimate some elliptic segments in these branches.