Dynamics around Simple Resonant Tori in Nearly Integrable Hamiltonian Systems

Abstract

By an application of the K.A.M. theory, we derive an accurate normal form valid in the vicinity of partially hyperbolic tori which arise close to simple resonances in nearly integrable Hamiltonian systems. This normal form allows to detect orbits homoclinic to a persistent torus. Moreover, it also gives precise estimates on the times of transition around the stable and unstable manifolds of these tori. Hence, we provide an efficient tool to compute the speed of drift of orbits shadowing a chain of hyperbolic tori associated to a simple resonant curve in the action space.