Diffusion approximation for noise-induced evolution of first integrals in multifrequency systems
arXiv:2006.16286 · doi:10.1007/s10955-021-02722-4
Abstract
We consider fast oscillating perturbations of dynamical systems in regions where one can introduce action-angle type coordinates. In an appropriate time scale, a diffusion approximation of the first-integrals evolution is described under the assumption that the set of resonance tori is small enough. If the action-angle coordinates can be introduced just piece-wise , the limiting diffusion process should be considered on an open book space. Such a process can be described by differential operators, one on each page, supplemented by some gluing conditions on the binding of the open book.
26 pages, will be submitted to Journal of Statistical Physics