{
  "id": "1205.2905",
  "version": "v8",
  "published": "2012-05-13T19:28:43.000Z",
  "updated": "2014-10-07T16:37:04.000Z",
  "title": "Uniqueness of the measure of maximal entropy for the squarefree flow",
  "authors": [
    "Ryan Peckner"
  ],
  "comment": "18 pages. Minor changes from previous version; to appear in Israel J. Math",
  "categories": [
    "math.DS",
    "math.NT"
  ],
  "abstract": "The squarefree flow is a natural dynamical system whose topological and ergodic properties are closely linked to the behavior of squarefree numbers. We prove that the squarefree flow carries a unique measure of maximal entropy and express this measure explicitly in terms of a skew-product of a Kronecker and a Bernoulli system. Using this characterization and a number-theoretic argument, we then show that the unique maximum entropy measure fails to possess the Gibbs property.",
  "revisions": [
    {
      "version": "v7",
      "updated": "2014-05-17T17:39:28.000Z",
      "comment": "18 pages. Several errors have been corrected; in particular, the proof of the Gibbs property in previous versions was incorrect. d-bar convergence of sofic approximations is also no longer necessary, and may not be provable with the present method. Structure of the proof has been completely changed in light of pre-existing work of Marcus and Newhouse",
      "journal": null,
      "doi": null
    },
    {
      "version": "v8",
      "updated": "2014-10-07T16:37:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B10",
      "28D20",
      "11N64",
      "11N69"
    ],
    "keywords": [
      "maximal entropy",
      "unique maximum entropy measure fails",
      "uniqueness",
      "squarefree flow carries",
      "unique measure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1205.2905P"
    }
  }
}