LOCAL ANALYSIS OF FORMAL STABILITY AND EXISTENCE OF FIXED-POINTS IN 4D SYMPLECTIC MAPPINGS

Symplectic mappings in a four-dimensional phase space are analysed; in the neighbourhood of an elliptic fixed point whose eigenvalues are cl ose to satisfy a double resonance condition, the perturbative tools of resonant normal forms are outlined. The analysis of the interpolating Hamiltonian of the normal form allows one to determine the existence and the stability of the fixed points which are due to the double reso nance: only some combinations of stabilities are allowed. Due to the a symptotic character of the series, the results are formal, but support ed by numerical computations.