This paper is devoted to the analysis of an extended neighborhood of the collinear equilibrium points of the Restricted Three Body Problem. The analysis is done using numerical tools for the determination of periodic orbits and invariant 2D tori. All the relevant information of the neutrally stable behavior of the dynamics in the vicinity of the three libration points is given. The results in this paper extend those given in \cite{jm-rtbp}, since they avoid the convergence restrictions of the semi--analytical approach used in this reference.