EVALUATION OF NONLINEAR RESONANCES IN 4D SYMPLECTIC MAPPINGS

We discuss the evaluation of the stability, position and width of reso nances in four-dimensional symplectic mappings. The approach presented in this paper is based on the computation of the resonant perturbativ e series carried out by the program ARES. This piece of code allows to perform the evaluation of the perturbative series and of the interpol ating Hamiltonian. Given a symplectic map in the neighbourhood of an e lliptic fixed point, the new code NERO performs the analysis of the or bits of the interpolating Hamiltonian both in the nonresonant and the resonant case. For each resonant normal form, the interpolating Hamilt onian is computed and the position and the stability of the resonant o rbits and the width of the islands are evaluated; this analysis is car ried out through the direct inspection of the coefficients of the inte rpolating Hamiltonian. All the computations are carried out at an arbi trary order; the first significant perturbative order is taken as a fi rst guess, and a Newton method is used to evaluate the higher orders e ffect. (C) 1998 IMACS/Elsevier Science B.V.