{
  "id": "1604.03365",
  "version": "v1",
  "published": "2016-04-12T12:20:47.000Z",
  "updated": "2016-04-12T12:20:47.000Z",
  "title": "Modulus of continuity of averages of SRB measures for a transversal family of piecewise expanding unimodal maps",
  "authors": [
    "Fabian Contreras"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "Let $f_t:[0,1] \\to [0,1]$ be a family of piecewise expanding unimodal maps with a common critical point that is dense for almost all $t \\in [a,b]$. If $\\mu_t$ is the corresponding SRB measure for $f_t$, we study the regularity of $\\Gamma(t)=\\int \\phi d\\mu_t$ when assuming that the family is transversal to the topological classes of these maps, more precisely, we prove that if $J_t(c)=\\sum_{k=0}^{\\infty} \\frac{v_t(f_t^k(c))}{Df_t^k(f_t(c))} \\neq 0$ for all $t$, where $v_t(x)=\\partial_s f_s(x)|_{s=t}$, then $\\Gamma(t)$ is not Lipschitz for almost all $t\\in [a,b]$. Furthermore, we give the exact modulus of continuity of $\\Gamma(t)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-04-12T12:20:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "piecewise expanding unimodal maps",
      "transversal family",
      "continuity",
      "exact modulus",
      "corresponding srb measure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160403365C"
    }
  }
}