{
  "id": "2107.12047",
  "version": "v1",
  "published": "2021-07-26T09:05:05.000Z",
  "updated": "2021-07-26T09:05:05.000Z",
  "title": "Expansive actions with specification of sofic groups, strong topological Markov property, and surjunctivity",
  "authors": [
    "Tullio Ceccherini-Silberstein",
    "Michel Coornaert",
    "Hanfeng Li"
  ],
  "categories": [
    "math.DS",
    "math.GR"
  ],
  "abstract": "A dynamical system is a pair $(X,G)$, where $X$ is a compact metrizable space and $G$ is a countable group acting by homeomorphisms of $X$. An endomorphism of $(X,G)$ is a continuous selfmap of $X$ which commutes with the action of $G$. One says that a dynamical system $(X,G)$ is surjunctive provided that every injective endomorphism of $(X,G)$ is surjective (and therefore is a homeomorphism). We show that when $G$ is sofic, every expansive dynamical system $(X,G)$ with nonnegative sofic topological entropy and satisfying the weak specification and the strong topological Markov properties, is surjunctive.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-07-26T09:05:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B40",
      "37B10",
      "37D20",
      "20F65"
    ],
    "keywords": [
      "strong topological markov property",
      "sofic groups",
      "expansive actions",
      "dynamical system",
      "surjunctivity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}