TRANSPORT IN HAMILTONIAN-SYSTEMS AND ITS RELATIONSHIP TO THE LYAPUNOVTIME

The assumption that transport in a Hamiltonian system can be described as a normal diffusion process leads naturally to a power law dependen ce of the exit time, T-E, On the Lyapunov time, T-L=1/lambda, where by lambda we denote the maximal Lyapunov characteristic number, LCN. Sin ce transport in perturbed integrable Hamiltonian systems can be modele d as normal diffusion only in regions where most of the KAM tori are d estroyed, the power law dependence appears when the perturbation is st rong. In this way the dependence T-E similar to T-L(c), found numerica lly by Murison et al. (1994) for the motion of asteroids in the outer belt, can be naturally interpreted, since in this region it is well kn own that resonances are closely spaced and, therefore, it is expected that KAM tori are mostly destroyed. However there is no theoretical re ason why the exponent, c, should have a universal value. (C) 1996 Amer ican Astronomical Society.