R. Ishizaki et al., ANOMALOUS DIFFUSION AND MIXING OF CHAOTIC ORBITS IN HAMILTONIAN DYNAMIC-SYSTEMS, Progress of theoretical physics, 89(5), 1993, pp. 947-963
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.