{
  "id": "0705.4060",
  "version": "v2",
  "published": "2007-05-28T15:57:34.000Z",
  "updated": "2015-07-08T11:46:06.000Z",
  "title": "C*- Algebras and Thermodynamic Formalism",
  "authors": [
    "Ruy Exel",
    "Artur O. Lopes"
  ],
  "comment": "version updated",
  "categories": [
    "math.DS",
    "math.OA"
  ],
  "abstract": "We present a detailed exposition (for a Dynamical System audience) of the content of the paper: R. Exel and A. Lopes, $C^*$ Algebras, approximately proper equivalence relations and Thermodynamic Formalism, {\\it Erg. Theo. and Dyn. Syst.}, Vol 24, pp 1051-1082 (2004). We show only the uniqueness of the \\beta-KMS (in a certain C*-Algebra obtained from the operators acting in $L^2$ of a Gibbs invariant probability $\\mu$) and its relation with the eigen-probability $\\nu_\\beta$ for the dual of a certain Ruele operator. We consider an example for a case of Hofbauer type where there exist a Phase transition for the Gibbs state. There is no Phase transition for the KMS state.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-05-28T15:57:34.000Z",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-07-08T11:46:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A55",
      "37D35"
    ],
    "keywords": [
      "thermodynamic formalism",
      "phase transition",
      "approximately proper equivalence relations",
      "gibbs invariant probability",
      "kms state"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0705.4060E"
    }
  }
}