FORCED SECONDARY RESONANCES AT THE 3 1 COMMENSURABILITY/

For the 3 : 1 Jovian resonance problem, the time scales of the two deg rees of freedom of the resonant Hamiltonian are well-separated [5]. Wi th the adiabatic approximation, the solution for the fast oscillations can be found in terms of the slowly varying variables. Thus the rapid ly oscillating terms in the slow oscillation equations can be treated as forced terms. We refer to the resonance between the forcing and int rinsic frequencies as a forced secondary one in this paper. We discuss the forced secondary resonances in asteroidal motion at the 3 : 1 com mensurability by using Wisdom's method. The results show that the orbi ts situated originally near the resonance will leave the neighbourhood of resonance and tend to the separatrices and critical points for dif ferent energies, respectively. We have not found any stochastic web as expected in this case. Moreover, we study the problem of validity on the approximation of a system.