{
  "id": "1508.02700",
  "version": "v1",
  "published": "2015-08-11T19:28:49.000Z",
  "updated": "2015-08-11T19:28:49.000Z",
  "title": "Linear response for intermittent maps",
  "authors": [
    "V. Baladi",
    "M. Todd"
  ],
  "categories": [
    "math.DS",
    "nlin.CD"
  ],
  "abstract": "We consider the one parameter family a-> T_a (a in [0,1]) of Pomeau-Manneville type interval maps introduced by Liverani-Saussol-Vaienti, with their associated absolutely continuous invariant probability measure m_a. For a in (0,1), Sarig and Gou\\\"ezel proved that the system mixes only polynomially (in particular, there is no spectral gap). We show that for any bounded observable g the map sending a to the average of g with respect to m_a is differentiable on [0,1/2), and we give a (linear response) formula for the value of the derivative. This is the first time that a linear response formula is obtained for slowly mixing dynamics. Our argument shows how cone techniques can be used to achieve linear response.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-08-11T19:28:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37C40",
      "37C30",
      "37E05"
    ],
    "keywords": [
      "intermittent maps",
      "pomeau-manneville type interval maps",
      "achieve linear response",
      "absolutely continuous invariant probability measure",
      "linear response formula"
    ],
    "publication": {
      "doi": "10.1007/s00220-016-2577-z",
      "journal": "Communications in Mathematical Physics",
      "year": 2016,
      "month": "Feb",
      "pages": 42
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016CMaPh.tmp...42B"
    }
  }
}