Isolating blocks near the collinear relative equilibria of the three-body problem

Rick Moeckel, Mathematics, University of Minnesota

The collinear relative equilibria are among the few explicitly known periodic solutions of the Newtonian three-body problem. It can be shown by standard perturbation methods that when the energy and angular momentum constants are varied slightly these periodic orbits become normally hyperbolic invariant spheres whose stable and unstable manifolds form separatrices in the integral manifolds. I will discuss a topological method for showing that the invariant set and its separatrices continue to exist for levels of energy and angular momentum far from those of the relative equilibrium.