{
  "id": "1806.06398",
  "version": "v1",
  "published": "2018-06-17T15:45:13.000Z",
  "updated": "2018-06-17T15:45:13.000Z",
  "title": "Diffusion limit for a slow-fast standard map",
  "authors": [
    "Alex Blumenthal",
    "Jacopo De Simoi",
    "Ke Zhang"
  ],
  "comment": "23 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "Consider the map $(x, y) \\mapsto (x + \\epsilon^{-\\alpha} \\sin (2\\pi x) + \\epsilon^{-1-\\alpha}z, z + \\epsilon \\sin(2\\pi x))$, which is conjugate to the Chirikov standard map with a large parameter. The parameter value $\\alpha = 1$ is related to \"scattering by resonance\" phenomena. For suitable $\\alpha$, we obtain a central limit theorem for the slow variable $z$ for a (Lebesgue) random initial condition. The result is proved by conjugating to the Chirikov standard map and utilizing the formalism of standard pairs. Our techniques also yield for the Chirikov standard map a related limit theorem and a \"finite-time\" decay of correlations result.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-06-17T15:45:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "slow-fast standard map",
      "chirikov standard map",
      "diffusion limit",
      "random initial condition",
      "central limit theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}