Claude Froeschle'

First numerical evidence of global Arnold diffusion in quasi--integrable systems

We provide numerical evidence of global diffusion occurring in slightly perturbed integrable Hamiltonian systems and symplectic maps. We show that even if a system is sufficiently close to be integrable, global diffusion occurs on a set with peculiar topology, the so--called Arnold web, and is qualitatively different from Chirikov diffusion, occurring in more perturbed systems.