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This paper presents methodology for the computation of whole sets ofheteroclinic connections between iso-energetic slices of center manifolds ofcenter x center x saddle fixed points of autonomous Hamiltonian systems. Itinvolves: (a) computing Taylor expansions of the center-unstable andcenter-stable manifolds of the departing and arriving fixed points through theparameterization method, using a new style that uncouples the center part fromthe hyperbolic one, thus making the fibered structure of the manifoldsexplicit; (b) uniformly meshing iso-energetic slices of the center manifolds,using a novel strategy that avoids numerical integration of the reduceddifferential equations and makes an explicit 3D representation of these slicesas deformed solid ellipsoids; (c) matching the center-stable andcenter-unstable manifolds of the departing and arriving points in a Poincar\'esection. The methodology is applied to obtain the whole set of iso-energeticheteroclinic connections from the center manifold of L2 to the center manifoldof L1 in the Earth-Moon circular, spatial Restricted Three-Body Problem, fornine increasing energy levels that reach the appearance of Halo orbits in bothL1 and L2. Some comments are made on possible applications to space missiondesign.

Semi-analytical computation of heteroclinic connections between center manifolds with the parameterization method