COMPARATIVE-STUDY OF THE ASTEROIDAL MOTION IN THE 3 2 AND 2/1 RESONANCES WITH JUPITER .1. PLANAR MODEL/

The long-period behavior of the asteroids in the 3:2 and 2:1 resonance s with Jupiter is investigated by integrating numerically the equation s of motion of the planar three-body system. The results of the numeri cal integration procedure were submitted to a low-pass filtering and t he decimation parameter was chosen in accordance with the filter. The behaviour of the most important physical quantities which describe the orbital evolution in the resonance were Fourier analysed. The topolog y of phase space was studied by constructing the surfaces of section. The structure of the phase space in the 3:2 and 2:1 resonances showed the presence of both regular and chaotic motion. Regular motion shows a great variety of orbital behaviour. Chaotic motion occurs because of : (1) the proximity of the resonance border; (2) the presence of secon dary resonances (when the one fundamental frequency enters into resona nce with the other frequencies and creates a pattern of islands inside the primary resonance); (3) the proximity of the chaotic region emana ting from the boundary of corotations. The location of the main second ary resonances was computed on the (a(0),e(0))-plane. The results obta ined with our numerical technique were compared to similar results pre viously obtained with either analytical or semi-numerical models by se veral authors.