Long-term evolution of the asteroid orbits at the 3:1 mean motion resonance with Jupiter (planar problem)

The 3:1 mean-motion resonance of the planar elliptic restricted three body problem (Sun-Jupiter-asteroid) is considered. The double numeric averaging is used to obtain the evolutionary equations which describe the long-term behavior of the asteroid's argument of pericentre and eccentricity. The existence of the adiabatic chaos area in the system's phase space is shown.