{
  "id": "2108.06724",
  "version": "v1",
  "published": "2021-08-15T11:36:34.000Z",
  "updated": "2021-08-15T11:36:34.000Z",
  "title": "Graph maps with zero topological entropy and sequence entropy pairs",
  "authors": [
    "Jian Li",
    "Xianjuan Liang",
    "Piotr Oprocha"
  ],
  "comment": "14 pages. Published online in Proc. Amer. Math. Soc",
  "doi": "10.1090/proc/15578",
  "categories": [
    "math.DS"
  ],
  "abstract": "We show that graph map with zero topological entropy is Li-Yorke chaotic if and only if it has an NS-pair (a pair of non-separable points containing in a same solenoidal $\\omega$-limit set), and a non-diagonal pair is an NS-pair if and only if it is an IN-pair if and only if it is an IT-pair. This completes characterization of zero topological sequence entropy for graph maps.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-15T11:36:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37E10",
      "37B40",
      "54H15"
    ],
    "keywords": [
      "zero topological entropy",
      "sequence entropy pairs",
      "graph map",
      "zero topological sequence entropy",
      "li-yorke chaotic"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}