DYNAMICS OF THE ASTEROIDAL 2/1-RESONANCE

The structure of the phase space of the 2/1 resonance case of the planar averaged asteroidal three-body problem is shown. The only chaotic regions found are the well-known chaotic region associated to secondary resonances, confined to low eccentricities, and the chaotic region associated to large libration amplitudes. Elsewhere, the Lyapunov times are generally large and only indicate some slow chaos in high eccentricities. When the full four-body Sun-Jupiter-Saturn-asteroid model is considered, chaos becomes the rule among 2/1 resonant orbits. Typical Lyapunov times in this case are less than 105 yr. The meaning of this result is discussed in the light of the few known results on dynamical systems with three or more degrees of freedom.