The invariant manifold structure of the spatial Hill's problem

Abstract

The paper studies the invariant manifolds of the spatial Hill's problem associated to the two liberation points. A combination of analytical and numerical tools allow the normalization of the Hamiltonian and the computation of periodic and quasi-periodic (invariant tori) orbits. With these tools, it is possible to give a complete description of the center manifolds, association to the liberation points, for a large set of energy values. A systematic exploration of the homoclinic and heteroclinic connections between the center manifolds of the liberation points is also given.