Transport in Hamiltonian Systems and its Relationship to the Lyapunov Time

Details Transport in Hamiltonian Systems and its Relationship to the Lyapunov Time Transport in Hamiltonian Systems and its Relationship to the Lyapunov Time

Apr 1996

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1996aj....111.1718v&link_type=abstract

Astronomical Journal v.111, p.1718

Astronomy and Astrophysics

Astronomy

13

Diffusion, Minor Planets

Scientific paper

The assumption that transport in a Hamiltonian system can be described as a normal diffusion process leads naturally to a power law dependence of the exit time, TE, on the Lyapunov time, TL=l/λ, where by λ we denote the maximal Lyapunov characteristic number, LCN. Since transport in perturbed integrable Hamiltonian systems can be modeled as normal diffusion only in regions where most of the KAM tori are destroyed, the power law dependence appears when the perturbation is strong. In this way the dependence TE˜TcL, found numerically 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 known that resonances are closely spaced and, therefore, it is expected that KAM tori are mostly destroyed. However there is no theoretical reason why the exponent, c, should have a universal value.

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