{
  "id": "1806.00214",
  "version": "v1",
  "published": "2018-06-01T06:48:50.000Z",
  "updated": "2018-06-01T06:48:50.000Z",
  "title": "Topological Markov chains of given entropy and period with or without measure of maximal entropy",
  "authors": [
    "Sylvie Ruette"
  ],
  "comment": "6 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "We show that, for every positive real number h and every positive integer p, there exist oriented graphs G, G' (with countably many vertices) that are strongly connected, of period p, of Gurevich entropy h, such that G is positive recurrent (thus the topological Markov chain on G admits a measure of maximal entropy) and G' is transient (thus the topological Markov chain on G' admits no measure of maximal entropy).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-06-01T06:48:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B10",
      "37B40"
    ],
    "keywords": [
      "topological markov chain",
      "maximal entropy",
      "gurevich entropy",
      "positive real number",
      "oriented graphs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}