ANOMALOUS DIFFUSION AND MIXING OF CHAOTIC ORBITS IN HAMILTONIAN DYNAMIC-SYSTEMS

Anomalous behaviors of the diffusion and mixing of chaotic orbits due to the intermittent sticking to the islands of normal tori and acceler ator-mode tori in a widespread chaotic sea are studied numerically and theoretically for Hamiltonian systems with two degrees of freedom. Th e probability distribution functions for the coarse-grained velocity ( characterizing the diffusion) and the coarse-grained expansion rate (c haracterizing the mixing) turn out to obey an anomalous scaling law wh ich is quite different from the Gaussian. The scaling law is confirmed for both diffusion and mixing by numerical experiments on the heating map introduced by Karney, which exhibits remarkable statistical prope rties more clearly than the standard map. Its scaling exponents for th e two cases, however, are found to be different from each other.