{
  "id": "2009.00925",
  "version": "v1",
  "published": "2020-09-02T10:04:09.000Z",
  "updated": "2020-09-02T10:04:09.000Z",
  "title": "Some properties of circle maps with zero topological entropy",
  "authors": [
    "Yini Yang"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "For a circle map $f\\colon\\mathbb{S}\\to\\mathbb{S}$ with zero topological entropy, we show that a non-diagonal pair $\\langle x,y\\rangle\\in \\mathbb{S}\\times \\mathbb{S}$ is non-separable if and only if it is an IN-pair if and only if it is an IT-pair. We also show that if a circle map is topological null then the maximal pattern entropy of every open cover is of polynomial order.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-02T10:04:09.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "zero topological entropy",
      "circle map",
      "properties",
      "non-diagonal pair",
      "maximal pattern entropy"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}