ar X iv : a st ro - p h / 02 10 02 6 v 1 1 O ct 2 00 2 From Fermi - Pasta - Ulam Problem to Galaxies : The Quest for Relaxation

The major problem posed by the Fermi-Pasta-Ulam work was the relaxation (thermalization) of a many-body system. We review two approaches to this problem, the ergodic theory and Langevin (stochastic) equation ones, which have been applied for the description of statistical mechanics of stellar systems. Among the particular problems that we consider, are 1-dimensional long-range interacting systems and iterated maps and 3-dimensional N-body gravitating systems. 1 The Fermi-Pasta-Ulam system: Historical introduction The numerical experiment by Fermi, Pasta and Ulam opened several new fields of research and appeared to be an invaluable source of inspiration for generations of physicists. This work is outstanding at least by the following reasons: 1. It represents the first computer study of a nonlinear system; 2. The results contradicted the belief held since Poincare. Fermi had considered it 'a little discovery' (as quoted by Ulam), thus immediately evaluating their extraordinary importance; 3. It was one of last Fermi's works, completed after his ultimate death in 1954; 4. Remained unpublished during a decade; 5. Coincides in time with Kolmogorov's theorem (1954), though FPU and Kolmogorov-Arnold-Moser (KAM) theory 'met' only in 1966. 6. Inspired the discovery of solitons and numerous other studies; 7. Its results are not fully understood till now and the FPU model continues its inspiring mission also today, after half a century. The circumstances around this work are now widely known, mainly due to the reminiscences of Fermi's collaborator of Los Alamos period and coau-thor of this and other works, renown mathematician Stanislav Ulam. We 1