{
  "id": "0903.1426",
  "version": "v1",
  "published": "2009-03-08T14:04:41.000Z",
  "updated": "2009-03-08T14:04:41.000Z",
  "title": "Gibbs and equilibrium measures for some families of subshifts",
  "authors": [
    "Tom Meyerovitch"
  ],
  "comment": "19 pages",
  "categories": [
    "math.DS",
    "math-ph",
    "math.MP"
  ],
  "abstract": "For SFTs, any equilibrium measure is Gibbs, as long a $f$ has $d$-summable variation. This is a theorem of Lanford and Ruelle. Conversely, a theorem of Dobru{\\v{s}}in states that for strongly-irreducible subshifts, shift-invariant Gibbs-measures are equilibrium measures. Here we prove a generalization of the Lanford-Ruelle theorem: for all subshifts, any equilibrium measure for a function with $d$-summable variation is \"topologically Gibbs\". This is a relaxed notion which coincides with the usual notion of a Gibbs measure for SFTs. In the second part of the paper, we study Gibbs and equilibrium measures for some interesting families of subshifts: $\\beta$-shifts, Dyck-shifts and Kalikow-type shifts (defined below). In all of these cases, a Lanford-Ruelle type theorem holds. For each of these families we provide a specific proof of the result.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-03-08T14:04:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B10",
      "37D35"
    ],
    "keywords": [
      "equilibrium measure",
      "lanford-ruelle type theorem holds",
      "summable variation",
      "gibbs measure",
      "usual notion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0903.1426M"
    }
  }
}