{
  "id": "2005.02038",
  "version": "v1",
  "published": "2020-05-05T10:06:15.000Z",
  "updated": "2020-05-05T10:06:15.000Z",
  "title": "Intrinsic Ergodicity of the negative beta-shift",
  "authors": [
    "Florent Nguema-Ndong"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "Let $ \\beta $ be a real less than -1. In this paper, we prove the unicity of the measure with maximal entropy of the negative $\\beta$-shift. Endowed with the shift, this symbolic dynamical system is coded under certain conditions, but in all case, it is shown that the measure with maximal entropy is carried by a support coded by a recurrent positive code. One of the difference between the positive and the negative $\\beta$-shift is the existence of gaps in the system for certain negative values of $ \\beta $ . It is about of intervals of negative $\\beta$-representations (cylinders) negligible with respect to the measure with maximal entropy. Nervertheless, this measure is a measure of Champernown.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-05T10:06:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11K16",
      "37A05",
      "37A25",
      "37B10"
    ],
    "keywords": [
      "intrinsic ergodicity",
      "negative beta-shift",
      "maximal entropy",
      "symbolic dynamical system",
      "recurrent positive code"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}