{
  "id": "2006.16286",
  "version": "v1",
  "published": "2020-06-29T18:06:47.000Z",
  "updated": "2020-06-29T18:06:47.000Z",
  "title": "Diffusion approximation for noise-induced evolution of first integrals in multifrequency systems",
  "authors": [
    "M. I. Freidlin",
    "A. D. Wentzell"
  ],
  "comment": "26 pages, will be submitted to Journal of Statistical Physics",
  "categories": [
    "math.PR"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-29T18:06:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "diffusion approximation",
      "multifrequency systems",
      "first integrals",
      "noise-induced evolution",
      "open book space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}