CHAOS IN THE 1-2-3 HAMILTONIAN NORMAL-FORM

The normal form of the Hamiltonian 1:2:3 resonance to degree 3 contains seven families of periodic solutions of which one can be complex unstable. Associated with this complex unstable solution is an invariant manifold N on which the dynamics can be characterised completely; one of the ingredients of N is a set of homoclinic orbits. In the normal form to degree 4 the set of homoclinic orbits breaks up, for certain parameter values, into one homoclinic orbit. This enables us to apply Šilnikov-Devaney theory to prove, at this stage numerically, the existence of a horseshoe map in the system with the implication of non-integrability and chaos in the normal form. © 1990.