{
  "id": "1508.06571",
  "version": "v1",
  "published": "2015-08-26T16:57:04.000Z",
  "updated": "2015-08-26T16:57:04.000Z",
  "title": "Linear response for intermittent maps with summable and nonsummable decay of correlations",
  "authors": [
    "Alexey Korepanov"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We consider a family of Pomeau-Manneville type interval maps $T_\\alpha$, parametrized by $\\alpha \\in (0,1)$, with the unique absolutely continuous invariant probability measures $\\nu_\\alpha$, and rate of correlations decay $n^{1-1/\\alpha}$. We show that despite the absence of a spectral gap for all $\\alpha \\in (0,1)$ and despite nonsummable correlations for $\\alpha \\geq 1/2$, the map $\\alpha \\mapsto \\int \\varphi \\, d\\nu_\\alpha$ is continuously differentiable for $\\varphi \\in L^{q}[0,1]$ for $q$ sufficiently large.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-08-26T16:57:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "linear response",
      "intermittent maps",
      "nonsummable decay",
      "correlations",
      "pomeau-manneville type interval maps"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150806571K"
    }
  }
}