{
  "id": "1703.10013",
  "version": "v1",
  "published": "2017-03-29T12:54:37.000Z",
  "updated": "2017-03-29T12:54:37.000Z",
  "title": "On pointwise periodicity in tilings, cellular automata and subshifts",
  "authors": [
    "Tom Meyerovitch",
    "Ville Salo"
  ],
  "comment": "23 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "We study implications of expansiveness and pointwise periodicity for certain groups and semigroups of transformations. Among other things we prove that every pointwise periodic finitely generated group of cellular automata is necessarily finite. We also prove that a subshift over any finitely generated group that consists of finite orbits is finite, and related results for tilings of Euclidean space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-29T12:54:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B05",
      "37B10",
      "37B15",
      "37B50"
    ],
    "keywords": [
      "cellular automata",
      "pointwise periodicity",
      "finite orbits",
      "pointwise periodic finitely generated group",
      "euclidean space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}