{
  "id": "1508.07553",
  "version": "v1",
  "published": "2015-08-30T10:57:32.000Z",
  "updated": "2015-08-30T10:57:32.000Z",
  "title": "Expansive actions of countable amenable groups with the Myhill property",
  "authors": [
    "Tullio Ceccherini-Silberstein",
    "Michel Coornaert"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:1506.06945",
  "categories": [
    "math.DS",
    "math.GR"
  ],
  "abstract": "Let $X$ be a compact metrizable space equipped with a continuous action of a countable amenable group $G$. Suppose that the dynamical system $(X,G)$ is expansive and is the quotient by a uniformly bounded-to-one factor map of a strongly irreducible subshift. Let $\\tau \\colon X \\to X$ be a continuous map commuting with the action of $G$. We prove that if there is no pair of distinct $G$-homoclinic points in $X$ having the same image under $\\tau$ then $\\tau$ is surjective.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-08-30T10:57:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37D20",
      "37B40",
      "37B10",
      "43A07"
    ],
    "keywords": [
      "countable amenable group",
      "myhill property",
      "expansive actions",
      "uniformly bounded-to-one factor map",
      "compact metrizable space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150807553C"
    }
  }
}