Evaluation of nonlinear resonances in 4D symplectic mappings

We discuss the evaluation of the stability, position and width of resonances in four-dimensional symplectic mappings. The approach presented in this paper is based on the computation of the resonant perturbative series carried out by the program ARES. This piece of code allows to perform the evaluation of the perturbative series and of the interpolating Hamiltonian. Given a symplectic map in the neighbourhood of an elliptic fixed point, the new code NERO performs the analysis of the orbits of the interpolating Hamiltonian both in the nonresonant and the resonant case. For each resonant normal form, the interpolating Hamiltonian is computed and the position and the stability of the resonant orbits and the width of the islands are evaluated; this analysis is carried out through the direct inspection of the coefficients of the interpolating Hamiltonian. All the computations are carried out at an arbitrary order; the first significant perturbative order is taken as a first guess, and a Newton method is used to evaluate the higher orders effect.