Diffusion in Hamiltonian quasi-integrable systems

The characterization of diffusion of orbits in Hamiltonian quasi- integrable systems is a relevant topic in dynamics. For quasi-integrable Hamiltonian systems a possible model for global diffusion, valid for perturbation larger than a critical value, was given by Chirikov; while for smaller perturbation the Nekhoroshev theorem leave the possibility of exponentially slow diffusion along a peculiar the Arnold’s web. We have studied this problem using a numerical approach. The aim of this chapter is to give the state of the art concerning the detection of slow Arnold’s diffusion in quasi-integrable Hamiltonian systems.