{
  "id": "1710.03706",
  "version": "v1",
  "published": "2017-10-10T16:26:11.000Z",
  "updated": "2017-10-10T16:26:11.000Z",
  "title": "Linear response for random dynamical systems",
  "authors": [
    "Wael Bahsoun",
    "Marks Ruziboev",
    "Benoî t Saussol"
  ],
  "categories": [
    "math.DS",
    "math-ph",
    "math.MP",
    "math.PR"
  ],
  "abstract": "We study for the first time linear response for random compositions of maps, chosen independently according to a distribution $\\mathbb P$. We are interested in the following question: how does an absolutely continuous stationary measure (acsm) of a random system change when $\\mathbb P$ changes smoothly to $\\mathbb P_{\\varepsilon}$? For a wide class of one dimensional random maps, we prove differentiability of acsm with respect to $\\varepsilon$; moreover, we obtain a linear response formula. We apply our results to iid compositions of uniformly expanding circle maps, to iid compositions of the Gauss-R\\'enyi maps (random continued fractions) and to iid compositions of Pomeau-Manneville maps.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-10T16:26:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "random dynamical systems",
      "iid compositions",
      "first time linear response",
      "dimensional random maps",
      "linear response formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}