The dynamics around the collinear point L3 of the RTBP

We consider the Restricted Three Body Problem (RTBP), and we restrict our attention to the equilibrium point L3. Our aim is centered in the description, as global as possible, of the dynamics around this equilibrium point. In this communication, we initially consider small values of µ, for which homoclinic connections to the equilibrium point L3 are horseshoe-shaped, and then, other values of µ are considered. We compute the objects in the center manifold of L3, including the invariant manifolds associated with them. They are computed by purely numerical procedures, in order to avoid the convergence restrictions of the semi-analytical ones (typically used around L1 or L2). We deal with homoclinic connections of periodic orbits and develop some numerical tools in order to compute them. These tools can be extended to compute also homoclinic connections to invariant tori.