{
  "id": "math/0612480",
  "version": "v2",
  "published": "2006-12-17T04:00:35.000Z",
  "updated": "2006-12-19T19:15:16.000Z",
  "title": "Measurable Sensitivity",
  "authors": [
    "Jennifer James",
    "Thomas Koberda",
    "Kathryn Lindsey",
    "Cesar E. Silva",
    "Peter Speh"
  ],
  "journal": "Proc. Amer. Math. Soc. 136 (2008), no. 10, 3549--3559",
  "categories": [
    "math.DS"
  ],
  "abstract": "We introduce the notion of measurable sensitivity, a measure-theoretic version of the condition of sensitive dependence on initial conditions. It is a consequence of light mixing, implies a transformation has only finitely many eigenvalues, and does not exist in the infinite measure-preserving case. Unlike the traditional notion of sensitive dependence, measurable sensitivity carries up to measure-theoretic isomorphism, thus ignoring the behavior of the function on null sets and eliminating dependence on the choice of metric.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-12-19T19:15:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A05"
    ],
    "keywords": [
      "sensitive dependence",
      "measure-theoretic version",
      "null sets",
      "infinite measure-preserving case",
      "measure-theoretic isomorphism"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "Proc. Amer. Math. Soc."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....12480J"
    }
  }
}