Study of chaos in Hamiltonian systems via convergent normal forms

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