Flow reconstruction and invariant tori in the spatial three-body problem

We deal with the spatial three-body problem in the various regimes where the Hamiltonian is split as the sum of two Keplerian systems plus a small perturbation. By averaging over the mean anomalies, truncating higher-order terms and using singular reduction theory we get a one-degree-of-freedom Hamiltonian system. Departing from the analysis performed in [39] concerning the relative equilibria of this reduced system, we carry out the reconstruction of the KAM tori surrounding the motions associated to each elliptic equilibrium. The existence of five-dimensional KAM tori for the spatial three-body problem is established. These tori surround various types of motions, from circular to near rectilinear, passing through coplanar or perpendicular.