{
  "id": "1507.08191",
  "version": "v1",
  "published": "2015-07-29T15:42:59.000Z",
  "updated": "2015-07-29T15:42:59.000Z",
  "title": "Spectral Gap and quantitative statistical stability for systems with contracting fibers and Lorenz like maps",
  "authors": [
    "Stefano Galatolo",
    "Rafael Lucena"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We consider transformations preserving a contracting foliation, such that the associated quotient map satisfies a Lasota Yorke inequality. We prove that the associated transfer operator, acting on suitable normed spaces, has spectral gap. As an application we consider Lorenz-Like two dimensional maps (piecewise hyperbolic with unbounded contraction and expansion rate): we prove that those systems have spectral gap and we show a quantitative estimation for their statistical stability. Under deterministic perturbations of the system, the physical measure varies continuously, with a modulus of continuity $O(\\delta \\log \\delta ).$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-07-29T15:42:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37C30",
      "37D50",
      "37A30"
    ],
    "keywords": [
      "spectral gap",
      "quantitative statistical stability",
      "contracting fibers",
      "associated quotient map satisfies",
      "lasota yorke inequality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150708191G"
    }
  }
}