{
  "id": "2306.02310",
  "version": "v1",
  "published": "2023-06-04T09:31:24.000Z",
  "updated": "2023-06-04T09:31:24.000Z",
  "title": "Linear response for intermittent maps with critical point",
  "authors": [
    "Juho Leppänen"
  ],
  "comment": "31 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "We consider a two-parameter family of maps $T_{\\alpha, \\beta} : [0,1] \\to [0,1]$ with a neutral fixed point and a non-flat critical point. Building on a cone technique due to Baladi and Todd, we show that for a class of $L^q$ observables $\\phi : [0,1] \\to \\mathbb{R}$, the bivariate map $(\\alpha, \\beta) \\mapsto \\int_0^1 \\phi \\, d\\mu_{\\alpha,\\beta}$, where $\\mu_{\\alpha, \\beta}$ denotes the invariant SRB measure, is differentiable in a certain parameter region, and establish a formula for its directional derivative.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-06-04T09:31:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A05",
      "37E05"
    ],
    "keywords": [
      "intermittent maps",
      "linear response",
      "invariant srb measure",
      "neutral fixed point",
      "bivariate map"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}