{
  "id": "1101.1750",
  "version": "v2",
  "published": "2011-01-10T09:46:36.000Z",
  "updated": "2018-01-02T12:36:25.000Z",
  "title": "On images of sofic systems",
  "authors": [
    "Wolfgang Krieger"
  ],
  "comment": "21 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "Let $\\Sigma$ and $\\bar\\Sigma$ be finite alphabets. For topologically transitive sofic systems $ X\\subset \\Sigma^{\\Bbb Z}$ and $\\widetilde X\\subset \\widetilde\\Sigma^{\\Bbb Z}$ we give a necessary and sufficient condition for the existence of a homomorphism from $X$ to $\\widetilde X$. For topologically mixing sofic systems $X \\subset \\Sigma^{\\Bbb Z}$ and $\\widetilde X\\subset \\widetilde\\Sigma^{\\Bbb Z}$, such that the topological entropy of $\\widetilde X$ is less than the topological entropy of $X$, we give a necessary and sufficient condition for the existence of a homomorphism of $X$ onto $\\widetilde X$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-01-10T09:46:36.000Z",
      "abstract": "Let $\\Sigma$ and $\\bar\\Sigma$ be fnite alphabets. For a topologically transitive sofic system $ X\\subset \\Sigma^{\\Bbb Z}$ and a sofic system $\\bar X\\subset \\bar\\Sigma^{\\Bbb Z}$ we give a necessary and sufficient condition for the existence of a homomorphism from $X$ to $\\bar X$. For a topologically transitive sofic system $X \\subset \\Sigma^{\\Bbb Z}$ and a topologically transitive aperiodic sofic system $\\bar X\\subset \\bar\\Sigma^{\\Bbb Z}$ we give a necessary and sufficient condition for the existence of a homomophism of $X$ onto $\\bar X$.",
      "comment": "22 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2018-01-02T12:36:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B10"
    ],
    "keywords": [
      "topologically transitive sofic system",
      "sufficient condition",
      "topologically transitive aperiodic sofic system",
      "fnite alphabets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1101.1750K"
    }
  }
}