Biasymptotic solutions of perturbed integrable Hamiltonian systems

Abstract

We prove that small perturbations of a real analytic integrable Hamiltonian system ind degrees of freedom generically have biasymptotic orbits which are obtained as intersections of the stable and unstable manifolds of invariant hyperbolic tori of dimensiond−1. Hence, these solutions will be forward and backward asymptotic to such a torus and not to a periodic solution. The generic condition, which is open and dense, is given by an explicit condition on the averaged perturbation.