{
  "id": "0910.1958",
  "version": "v2",
  "published": "2009-10-10T23:41:30.000Z",
  "updated": "2011-11-07T00:10:53.000Z",
  "title": "On μ-Compatible Metrics and Measurable Sensitivity",
  "authors": [
    "Ilya Grigoriev",
    "Nathaniel Ince",
    "Marius Catalin Iordan",
    "Amos Lubin",
    "Cesar E. Silva"
  ],
  "comment": "Many improvements in exposition, a technical assumption removed, as suggested by the reviewer",
  "journal": "Colloq. Math. 126 (2012), 53-72",
  "doi": "10.4064/cm126-1-3",
  "categories": [
    "math.DS"
  ],
  "abstract": "We introduce the notion of W-measurable sensitivity, which extends and strictly implies canonical measurable sensitivity, a measure- theoretic version of sensitive dependence on initial conditions. This notion also implies pairwise sensitivity with respect to a large class of metrics. We show that nonsingular ergodic and conservative dynamical systems on standard spaces must be either W-measurably sensitive, or isomorphic mod 0 to a minimal uniformly rigid isometry. In the finite measure-preserving case they are W-measurably sensitive or measurably isomorphic to an ergodic isometry on a compact metric space.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-11-07T00:10:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "compact metric space",
      "minimal uniformly rigid isometry",
      "strictly implies canonical measurable sensitivity",
      "ergodic isometry",
      "theoretic version"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0910.1958G"
    }
  }
}