Diffusion Approximation for Noise-Induced Evolution of First Integrals in Multifrequency Systems

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 the first-integrals evolution is described under assumption that set resonance tori small enough. If coordinates be introduced just piece-wise , limiting process should considered on open book space. Such by differential operators, each page, supplemented some gluing conditions binding book.