On the Relationship Between Lyapunov Times and Macroscopic Instability Times

Details On the Relationship Between Lyapunov Times and Macroscopic Instability Times On the Relationship Between Lyapunov Times and Macroscopic Instability Times

Jan 1996

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1996cemda..63..227m&link_type=abstract

Celestial Mechanics & Dynamical Astronomy, Volume 63, Issue 2, pp.227-239

Astronomy and Astrophysics

Astronomy

24

Invariant Tori, Overlapping Of Resonances, Lyapunov Exponents, Diffusion Times, Random Walk

Scientific paper

On the basis of the general theory of Hamiltonian systems, we consider the relationship between Lyapunov times and macroscopic diffusion times. 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 case, the relationship is polynomial although we do not find any theoretical reason for the existence of a ‘universal’ power law. We show numerical evidences which confirm our theoretical considerations.

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