{
  "id": "2012.03409",
  "version": "v1",
  "published": "2020-12-07T01:38:56.000Z",
  "updated": "2020-12-07T01:38:56.000Z",
  "title": "Equilibrium states which are not Gibbs measure on hereditary subshifts",
  "authors": [
    "Zijie Lin",
    "Ercai Chen"
  ],
  "comment": "27 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "In this paper, we consider which kind of invariant measure on hereditary subshifts is not Gibbs measure. For the hereditary closure of a subshift $(X,S)$, we prove that in some situation, the invariant measure $\\nu*B_{p,1-p}$ can not be a Gibbs measure where $\\nu$ is an invariant measure on $(X,S)$. As an application, we show that for some $\\B$-free subshifts, the unique equilibrium state $\\nu_\\eta*B_{p,1-p}$ is not Gibbs measure.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-12-07T01:38:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "gibbs measure",
      "hereditary subshifts",
      "invariant measure",
      "unique equilibrium state",
      "free subshifts"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}