{
  "id": "2403.04456",
  "version": "v1",
  "published": "2024-03-07T12:51:39.000Z",
  "updated": "2024-03-07T12:51:39.000Z",
  "title": "On the stability and shadowing of tree-shifts of finite type",
  "authors": [
    "Dawid Bucki"
  ],
  "comment": "This is the Author Accepted Manuscript (AAM version of the paper that will appear in the Proceedings of the American Mathematical Society. This research was funded in part by National Science Centre (NCN), Poland grant no. 2022/47/O/ST1/03299",
  "categories": [
    "math.DS"
  ],
  "abstract": "We investigate relations between the pseudo-orbit-tracing property, topological stability and openness for tree-shifts. We prove that a tree-shift is of finite type if and only if it has the pseudo-orbit-tracing property which implies that the tree-shift is topologically stable and all shift maps are open. We also present an example of a tree-shift for which all shift maps are open but which is not of finite type. It also turns out, that if a topologically stable tree-shift does not have isolated points then it is of finite type.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-03-07T12:51:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B10",
      "37B51",
      "37B25",
      "37B65"
    ],
    "keywords": [
      "finite type",
      "shift maps",
      "pseudo-orbit-tracing property",
      "topological stability",
      "topologically stable tree-shift"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}