{
  "id": "1310.2740",
  "version": "v1",
  "published": "2013-10-10T09:23:09.000Z",
  "updated": "2013-10-10T09:23:09.000Z",
  "title": "Bowen's entropy-conjugacy conjecture is true up to finite index",
  "authors": [
    "Mike Boyle",
    "Jerome Buzzi",
    "Kevin Mcgoff"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "For a topological dynamical system consisting of a continuous map f, and a (not necessarily compact) subset Z of X, Bowen (1973) defined a dimension-like version of entropy, h_X(f,Z). In the same work, he introduced a notion of entropy-conjugacy for pairs of invertible compact systems: the systems (X,f) and (Y,g) are entropy-conjugate if there exist invariant Borel subsets X' of X and Y' of Y such that h_X(f,X\\setminus X') < h_X(f,X), h_Y(g,Y \\setminus Y') < h_Y(g,Y), and (X',f|_{X'}) is topologically conjugate to (Y',g|_{Y'}). Bowen conjectured that two mixing shifts of finite type are entropy-conjugate if they have the same entropy. We prove that two mixing shifts of finite type with equal entropy and left ideal class are entropy-conjugate. Consequently, in every entropy class Bowen's conjecture is true up to finite index.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-10-10T09:23:09.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bowens entropy-conjugacy conjecture",
      "finite index",
      "finite type",
      "entropy class bowens conjecture",
      "left ideal class"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.2740B"
    }
  }
}