{
  "id": "1508.02033",
  "version": "v1",
  "published": "2015-08-09T14:34:34.000Z",
  "updated": "2015-08-09T14:34:34.000Z",
  "title": "Central limit theorem for generalized Weierstrass functions",
  "authors": [
    "Amanda de Lima",
    "Daniel Smania"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "Let $f$ be a $C^{2+\\epsilon}$ expanding map of the circle and $v$ be a $C^{1+\\epsilon}$ real function of the circle. Consider the twisted cohomological equation $v(x) = \\alpha (f(x)) - Df(x) \\alpha (x)$ which has a unique bounded solution $\\alpha$. We prove that $\\alpha$ is either $C^{1+\\epsilon}$ or nowhere differentiable, and if $\\alpha$ is nowhere differentiable then the Newton quotients of $\\alpha$, after an appropriated normalization, converges in distribution to the normal distribution, with respect to the unique absolutely continuous invariant probability of $f$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-08-09T14:34:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37C30",
      "37C40",
      "37D50",
      "37E05",
      "37A05"
    ],
    "keywords": [
      "central limit theorem",
      "generalized weierstrass functions",
      "unique absolutely continuous invariant probability",
      "real function",
      "unique bounded solution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150802033D"
    }
  }
}