{
  "id": "1001.5323",
  "version": "v2",
  "published": "2010-01-29T04:56:44.000Z",
  "updated": "2011-04-15T13:57:27.000Z",
  "title": "Class Degree and Relative Maximal Entropy",
  "authors": [
    "Mahsa Allahbakhshi",
    "Anthony Quas"
  ],
  "comment": "30 pages, 7 figures",
  "journal": "Trans. Amer. Math. Soc. 365 (2013) 1347-1368",
  "categories": [
    "math.DS"
  ],
  "abstract": "Given a factor code $\\pi$ from a one-dimensional shift of finite type $X$ onto an irreducible sofic shift $Y$, if $\\pi$ is finite-to-one there is an invariant called the degree of $\\pi$ which is defined the number of preimages of a typical point in $Y$. We generalize the notion of the degree to the class degree which is defined for any factor code on a one-dimensional shift of finite type. Given an ergodic measure $\\nu$ on $Y$, we find an invariant upper bound on the number of ergodic measures on $X$ which project to $\\nu$ and have maximal entropy among all measures in the fibre $\\pi^{-1}\\{\\nu\\}$. We show that this bound and the class degree of the code agree when $\\nu$ is ergodic and fully supported. One of the main ingredients of the proof is a uniform distribution property for ergodic measures of relative maximal entropy.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-04-15T13:57:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B10"
    ],
    "keywords": [
      "relative maximal entropy",
      "class degree",
      "ergodic measure",
      "one-dimensional shift",
      "finite type"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "Trans. Amer. Math. Soc."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}