Graphical evolution of the Arnold web: From order to chaos

We represent graphically the evolution of the set of resonances of a quasi- integrable dynamical system, the so-called Arnold web, whose structure is c rucial for the stability properties of the system. The basis of our represe ntation is the use of an original numerical method, whose definition is dir ectly related to the dynamics of orbits, and the careful choice of a model system. We also show the transition from the Nekhoroshev stability regime t o the Chirikov diffusive one, which is a generic nontrivial phenomenon occu rring in many physical processes, such as slow chaotic transport in the ast eroid belt and beam-beam interaction.