STUDY OF CHAOS IN HAMILTONIAN-SYSTEMS VIA CONVERGENT NORMAL FORMS

We use Moser's normal forms to study chaotic motion in two-degree hami ltonian systems near a saddle point. Besides being convergent, they pr ovide a suitable description of the cylindrical topology of the chaoti c flow in that vicinity. Both aspects combined allowed a precise compu tation of the homoclinic interaction of stable and unstable manifolds in the full phase space, rather than just the Poincare section. The fo rmalism was applied to the Henon-Heiles hamiltonian, producing strong evidence that the region of convergence of these normal forms extends over that originally established by Moser.