Phase Diagram in Asteroidal Motion

In order to study the dynamical behaviour of asteroids in commensurability with a planet, we propose a phase diagram obtained by short computer time. We test this numerical procedure by analyzing the behaviour of real and fictitious asteroids in first order commensurabilities with Jupiter. We have also studied the evolution time of the orbital elements and other variables to compare these results with those obtained in the phase diagram. The results obtained with our numerical technique were compared to similar results previously obtained by other authors. This revised version was published online in July 2006 with corrections to the Cover Date.