  We describe a method for computing an atlas for the stable or unstable
manifold attached to an equilibrium point, and implement the method for the
saddle-focus libration points of the planar equilateral restricted four body
problem. We employ the method at the maximally symmetric case of equal masses,
where we compute atlases for both the stable and unstable manifolds. The
resulting atlases are comprised of thousands of individual chart maps, with
each chart represented by a two variable Taylor polynomial. Post-processing the
atlas data yields approximate intersections of the invariant manifolds, which
we refine via a shooting method for an appropriate two point boundary value
problem. Finally we apply numerical continuation to the BVPs. This breaks the
symmetries and leads to connecting orbits for some non-equal values of the
primary masses.
