Dynamical behavior of asteroids near resonance: The 4 : 1 gap and the 7 : 2 group

A comparative study of the evolution of the Sun-Jupiter-Asteroid system nea r the 4:1 and 7:2 resonances is performed by means of two techniques that p roceed differently from the Hamiltonian corresponding to the planar restric ted elliptic three-body problem. One technique is based on the classical Sc hubart averaging while the other is based on a mapping method in which the perturbing part of the Hamiltonian is expanded and the resulting terms are ordered according to a weight function that depends on the powers of eccent ricities and the coefficients of the terms. For the mapping method the effe ct of Saturn on the asteroidal evolution is introduced and the degree of ch aos is estimated by means of the Lyapunov time. Both methods are shown to l ead to similar results and can be considered a suitable tool for describing the evolution of asteroids in the Kirkwood gap and the group corresponding to the 4:1 and 7:2 Jovian resonances, respectively.