  This paper presents methodology for the computation of whole sets of
heteroclinic connections between iso-energetic slices of center manifolds of
center x center x saddle fixed points of autonomous Hamiltonian systems. It
involves: (a) computing Taylor expansions of the center-unstable and
center-stable manifolds of the departing and arriving fixed points through the
parameterization method, using a new style that uncouples the center part from
the hyperbolic one, thus making the fibered structure of the manifolds
explicit; (b) uniformly meshing iso-energetic slices of the center manifolds,
using a novel strategy that avoids numerical integration of the reduced
differential equations and makes an explicit 3D representation of these slices
as deformed solid ellipsoids; (c) matching the center-stable and
center-unstable manifolds of the departing and arriving points in a Poincar\'e
section. The methodology is applied to obtain the whole set of iso-energetic
heteroclinic connections from the center manifold of L2 to the center manifold
of L1 in the Earth-Moon circular, spatial Restricted Three-Body Problem, for
nine increasing energy levels that reach the appearance of Halo orbits in both
L1 and L2. Some comments are made on possible applications to space mission
design.
