MARGINAL RESONANCES AND INTERMITTENT BEHAVIOR IN THE MOTION IN THE VICINITY OF A SEPARATRIX

A condition upon which sporadic bursts (intermittent behaviour) of the relative energy become possible is derived for the motion in the chao tic layer around the separatrix of a non-linear resonance. This is a c ondition for the existence of a marginal resonance, i.e. a resonance l ocated at the border of the layer. A separatrix map in Chirikov's form [Chirikov, B. V., Phys. Reports 52, 263 (1979)] is used to describe t he motion. In order to provide a straightforward comparison with numer ic integrations, the separatrix map is synchronized to the surface of the section farthest from the saddle point. The condition of intermitt ency is applied to clear out the nature of the phenomenon of bursts of the eccentricity of chaotic asteroidal trajectories in the 3/1 mean m otion commensurability with Jupiter. On the basis of the condition, a new intermittent regime of resonant asteroidal motion is predicted and then identified in numeric simulations.