STABILITY AND GEOMETRY OF 3RD-ORDER RESONANCES IN 4-DIMENSIONAL SYMPLECTIC MAPPINGS

We analyze four-dimensional symplectic mappings in the neighbourhood o f an elliptic fixed point whose eigenvalues are close to satisfy a thi rd-order resonance. Using the perturbative tools of resonant normal fo rms, the geometry of the orbits and the existence of elliptic or hyper bolic one-dimensional tori (fixed lines) is worked out. This allows on e to give an analytical estimate of the stability domain when the reso nance is unstable. A comparison with numerical results for the four-di mensional Henon mapping is given.