On the "Blue sky catastrophe termination" in the restricted four-body problem

The restricted three-body problem posses the property that some classes of doubly asymptotic orbits are limits members of families of periodic orbits, this phenomena has been known as the "Blue Sky Catastrophe" termination. A similar case occurs in the restricted four body problem for the collinear equilibrium point named L2. We make an analytical and numerical study of the stable and unstable manifolds to verify that the hypothesis under which this phenomena occurs are satisfied.