Integral manifolds of the restricted three-body problem (Q2730717)

For the restricted three-body problem, plane and spatial, non-regularized and regularized, the authors compute the homology of integral manifold for each regular value of Jacobi constant. These computations show that the integral manifold undergoes a bifurcation at each critical value. The existence, in the spatial problem, of a critical point at infinity for Jacobi constant implies that, as in the full three-body problem, there are bifurcations of integral manifold which are not associated to relative equilibria. The authors use the homology tables computed for these four restricted problems to apply their own previous results on homological criteria for the existence of cross-sections with a given boundary, and of global cross-sections.