{
  "id": "1110.4921",
  "version": "v3",
  "published": "2011-10-21T22:42:25.000Z",
  "updated": "2011-11-30T11:00:10.000Z",
  "title": "On the density of periodic configurations in strongly irreducible subshifts",
  "authors": [
    "Tullio Ceccherini-Silberstein",
    "Michel Coornaert"
  ],
  "journal": "Nonlinearity 25 (2012), 2119-2131",
  "categories": [
    "math.DS",
    "math.GR"
  ],
  "abstract": "Let $G$ be a residually finite group and let $A$ be a finite set. We prove that if $X \\subset A^G$ is a strongly irreducible subshift of finite type containing a periodic configuration then periodic configurations are dense in $X$. The density of periodic configurations implies in particular that every injective endomorphism of $X$ is surjective and that the group of automorphisms of $X$ is residually finite. We also introduce a class of subshifts $X \\subset A^\\Z$, including all strongly irreducible subshifts and all irreducible sofic subshifts, in which periodic configurations are dense.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-11-30T11:00:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B10",
      "37B15",
      "37B50",
      "68Q80"
    ],
    "keywords": [
      "strongly irreducible subshift",
      "periodic configurations implies",
      "finite type",
      "finite set",
      "irreducible sofic subshifts"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1088/0951-7715/25/7/2119",
      "journal": "Nonlinearity",
      "year": 2012,
      "month": "Jul",
      "volume": 25,
      "number": 7,
      "pages": 2119
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012Nonli..25.2119C"
    }
  }
}