{
  "id": "1708.03965",
  "version": "v1",
  "published": "2017-08-13T21:16:27.000Z",
  "updated": "2017-08-13T21:16:27.000Z",
  "title": "Sensitive dependence of geometric Gibbs states",
  "authors": [
    "Daniel Coronel",
    "Juan Rivera-Letelier"
  ],
  "categories": [
    "math.DS",
    "math-ph",
    "math.MP"
  ],
  "abstract": "For quadratic-like maps, we show a phenomenon of sensitive dependence of geometric Gibbs states: There are analytic families of quadratic-like maps for which an arbitrarily small perturbation of the parameter can have a definite effect on the low-temperature geometric Gibbs states. Furthermore, this phenomenon is robust: There is an open set of analytic 2-parameter families of quadratic-like maps that exhibit sensitive dependence of geometric Gibbs states. We introduce a geometric version of the Peierls condition for contour models ensuring that the low-temperature Gibbs states are concentrated near the critical orbit.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-08-13T21:16:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "sensitive dependence",
      "quadratic-like maps",
      "low-temperature geometric gibbs states",
      "low-temperature gibbs states",
      "analytic families"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}