{
  "id": "1309.6340",
  "version": "v1",
  "published": "2013-09-24T20:39:22.000Z",
  "updated": "2013-09-24T20:39:22.000Z",
  "title": "Compensation functions for factors of shifts of finite type",
  "authors": [
    "John Antonioli"
  ],
  "comment": "20 pages, 1 figure submitted to Ergodic Theory Dyn. Syst",
  "categories": [
    "math.DS"
  ],
  "abstract": "We consider an infinite-to-one factor map from an irreducible shift of finite type X to a sofic shift Y. A compensation function relates equilibrium states on X to equilibrium states on Y. The p-Dini condition is given as a way of measuring the smoothness of a continuous function, with 1-Dini corresponding to functions with summable variation. Two types of compensation functions are defined in terms of this condition. We show that the relative equilibrium states of a 1-Dini function f over a fully supported invariant measure on Y are themselves fully supported, and have positive relative entropy. We then show that there exists a compensation function which is p-Dini for all p > 1 which has relative equilibrium states supported on a finite-to-one subfactor.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-09-24T20:39:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B10",
      "37D35"
    ],
    "keywords": [
      "finite type",
      "compensation function relates equilibrium states",
      "relative equilibrium states",
      "infinite-to-one factor map",
      "finite-to-one subfactor"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.6340A"
    }
  }
}