A symplectic mapping model as a tool to understand the dynamics of 2/1 resonant asteroid motion

We present a 3-D symplectic mapping model that is valid at the 2:1 mean mot ion resonance in the asteroid motion, in the Sun-Jupiter-asteroid model. Th is model is used to study the dynamics inside this resonance and several fe atures of the system have been made clear. The introduction of the third di mension, through the inclination of the asteroid orbit, plays an important role in the evolution of the asteroid and the appearance of chaotic motion. Also, the existence of the secondary resonances is clearly shown and their role in the appearance of chaotic motion and the slow diffusion of the ele ments of the orbit is demonstrated.