{
  "id": "math/0411494",
  "version": "v1",
  "published": "2004-11-22T18:50:49.000Z",
  "updated": "2004-11-22T18:50:49.000Z",
  "title": "Uniform endomorphisms which are isomorphic to a Bernoulli shift",
  "authors": [
    "Christopher Hoffman",
    "Daniel Rudolph"
  ],
  "comment": "23 pages, published version",
  "journal": "Ann. of Math. (2), Vol. 156 (2002), no. 1, 79--101",
  "categories": [
    "math.DS"
  ],
  "abstract": "A {\\it uniformly $p$-to-one endomorphism} is a measure-preserving map with entropy log $p$ which is almost everywhere $p$-to-one and for which the conditional expectation of each preimage is precisely $1/p$. The {\\it standard} example of this is a one-sided $p$-shift with uniform i.i.d. Bernoulli measure. We give a characterization of those uniformly finite-to-one endomorphisms conjugate to this standard example by a condition on the past tree of names which is analogous to {\\it very weakly Bernoulli} or {\\it loosely Bernoulli.} As a consequence we show that a large class of isometric extensions of the standard example are conjugate to it.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-11-22T18:50:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A35",
      "28D05",
      "37A05",
      "37B10"
    ],
    "keywords": [
      "bernoulli shift",
      "uniform endomorphisms",
      "standard example",
      "isomorphic",
      "uniformly finite-to-one endomorphisms conjugate"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Princeton University and the Institute for Advanced Study",
      "journal": "Ann. Math."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math.....11494H"
    }
  }
}