Long-time behavior of weakly coupled oscillators
The authors consider small perturbations of a simple completely integrable system with many degree of freedoms, that is called weakly coupled oscillators. They investigated the long-time behavior of the perturbed system, in particular, its slow motion part, which means the deviations from non-perturbed trajectories, within an appropriate time scale, and show that the limit behavior of slow motion is described as Markov process on the space associated with first integral of the non-perturbed system. The behavior of two weakly coupled oscillators is illustrated as an example.
scientific article; zbMATH DE number 5076312