{
  "id": "1603.09690",
  "version": "v1",
  "published": "2016-03-31T17:20:02.000Z",
  "updated": "2016-03-31T17:20:02.000Z",
  "title": "Linear and fractional response for the SRB measure of smooth hyperbolic attractors and discontinuous observables",
  "authors": [
    "Viviane Baladi",
    "Tobias Kuna",
    "Valerio Lucarini"
  ],
  "categories": [
    "math.DS",
    "math-ph",
    "math.MP",
    "nlin.CD"
  ],
  "abstract": "We consider a smooth one-parameter family t -> f_t of diffeomorphisms with compact transitive Axiom A attractors. Our first result is that for any function G in the Sobolev space H^r_p, with p>1 and 0<r<1/p, the map R(t) sending t to the average of G with respect to the SRB measure of f_t is s-H\\\"older continuous for all s <r. This applies to h(x)H(g(x)-a) (for all s<1) for h and g smooth and H the Heaviside function, if a is not a critical value of g. Our second result says that for any such function so that, in addition, the intersection of the set of points x so that g(x)=a with the support of h is foliated by \"admissible stable leaves\" of f_t, the map R(t) is differentiable. (We provide distributional linear response and fluctuation-dissipation formulas for the derivative.) Obtaining linear response or fractional response for such observables is motivated by extreme-value theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-03-31T17:20:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37C40",
      "37C30",
      "37D20"
    ],
    "keywords": [
      "smooth hyperbolic attractors",
      "fractional response",
      "srb measure",
      "discontinuous observables",
      "second result says"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160309690B"
    }
  }
}