ON THE RELATIONSHIP BETWEEN LYAPUNOV TIMES AND MACROSCOPIC INSTABILITY TIMES

On the basis of the general theory of Hamiltonian systems, we consider the relationship between Lyapunov times and macroscopic diffusion tim es. We find out that there are two regimes: the Nekhoroshev regime and the resonant overlapping regime. In the first case the diffusion time is exponentially long with respect to Lyapunov times. In the second c ase, the relationship is polynomial although we do not find any theore tical reason for the existence of a 'universal' power law. We show num erical evidences which confirm our theoretical considerations.