{
  "id": "2008.05679",
  "version": "v1",
  "published": "2020-08-13T04:01:08.000Z",
  "updated": "2020-08-13T04:01:08.000Z",
  "title": "Quantitative Statistical Stability for the Equilibrium States of Piecewise Partially Hyperbolic Maps",
  "authors": [
    "Rafael Bilbao",
    "Ricardo Bioni",
    "Rafael Lucena"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We consider a class of endomorphisms which contains a set of piecewise partially hyperbolic dynamics semi-conjugated to non-uniformly expanding maps. The aimed transformation preserves a foliation which is almost everywhere uniformly contracted with possible discontinuity sets, which are parallel to the contracting direction. We apply the spectral gap property and the $\\zeta$-H\\\"older regularity of the disintegration of its equilibrium state to prove a quantitative statistical stability statement. More precisely, under deterministic perturbations of the system of size $\\delta$, we show that the physical measure varies continuously with respect to a strong $L^\\infty$-like norm. Moreover, we prove that its modulus of continuity is $O(\\delta^\\zeta \\log \\delta)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-13T04:01:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A25",
      "37A10",
      "37C30",
      "37D50"
    ],
    "keywords": [
      "piecewise partially hyperbolic maps",
      "quantitative statistical stability",
      "equilibrium state",
      "partially hyperbolic dynamics",
      "spectral gap property"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}