INSTABILITY AND DIFFUSION IN THE ELLIPTIC RESTRICTED 3-BODY PROBLEM

The importance of the stability characteristics of the planar elliptic restricted three-body problem is that they offer insight about the ge neral dynamical mechanisms causing instability in celestial mechanics. To analyze these concerns, elliptic-elliptic and hyperbolic-elliptic resonance orbits (periodic solutions with lower period) are numericall y discovered by use of Newton's differential correction method. We fin d indications of stability for the elliptic-elliptic resonance orbits because slightly perturbed orbits define a corresponding two-dimension al invariant manifold on the Poincare surface-section. For the resonan ce orbit of the hyperbolic-elliptic type, we show numerically that its stable and unstable manifolds intersect transversally in phase-space to induce instability. Then, we find indications that there are orbits which jump from one resonance zone to the next before escaping to inf inity. This phenomenon is related to the so-called Arnold diffusion.