{
  "id": "1610.00672",
  "version": "v1",
  "published": "2016-10-03T18:50:30.000Z",
  "updated": "2016-10-03T18:50:30.000Z",
  "title": "Arcwise connectedness of the set of ergodic measures of hereditary shifts",
  "authors": [
    "Jakub Konieczny",
    "Michal Kupsa",
    "Dominik Kwietniak"
  ],
  "comment": "12 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "We show that the set of ergodic invariant measures of a shift space with a safe symbol (this includes all hereditary shifts) is arcwise connected when endowed with the $d$-bar metric. As a consequence the set of ergodic measures of such a shift is also arcwise connected in the weak-star topology and the entropy function over this set attains all values in the interval between zero and the topological entropy of the shift (inclusive).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-03T18:50:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B10",
      "37A05",
      "37A25",
      "37A30",
      "37A35",
      "37A45",
      "37C40"
    ],
    "keywords": [
      "ergodic measures",
      "hereditary shifts",
      "arcwise connectedness",
      "ergodic invariant measures",
      "set attains"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}