Some particularities of the collinear point L3 in the RTBP

We are interested in studying the motion in a (big) neighborhood of the collinear equilibrium point L3 of the RTBP. We consider both the planar and spatial cases. Actually different kinds of invariant objects appear: periodic orbits, invariant tori, the associated invariant manifolds, collision manifolds and homoclinic and hete-roclinic phenomena among others. In this communication, we just present some particularities of L3 and its 1-dimensional manifolds to show the difficulties that we have to cope with in order to give a global description of the motion in a global neighborhood of 3. Key words and expressions: Restricted three-body problem, equilibrium point, periodic orbits, invariant tori, manifolds.