  A condition upon which sporadic bursts (intermittent behaviour) of the
relative energy become possible is derived for the motion in the chaotic layer
around the separatrix of non-linear resonance. This is a condition for the
existence of a marginal resonance, i.e. a resonance located 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 the motion. In order to provide a
straightforward comparison with numeric integrations, the separatrix map is
synchronized to the surface of the section farthest from the saddle point. The
condition of intermittency is applied to clear out the nature of the phenomenon
of bursts of the eccentricity of chaotic asteroidal trajectories in the 3/1
mean motion 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.
