{
  "id": "1812.01066",
  "version": "v1",
  "published": "2018-12-03T20:25:52.000Z",
  "updated": "2018-12-03T20:25:52.000Z",
  "title": "Rationality is decidable for nearly Euclidean Thurston maps",
  "authors": [
    "William Floyd",
    "Walter Parry",
    "Kevin M. Pilgrim"
  ],
  "comment": "26 pages, 6 figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "Nearly Euclidean Thurston (NET) maps are described by simple diagrams which admit a natural notion of size. Given a size bound $C$, there are finitely many diagrams of size at most $C$. Given a NET map $F$ presented by a diagram of size at most $C$, the problem of determining whether $F$ is equivalent to a rational function is, in theory, a finite computation. We give bounds for the size of this computation in terms of $C$ and one other natural geometric quantity. This result partially explains the observed effectiveness of the computer program NETmap in deciding rationality.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-03T20:25:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F10",
      "57M12"
    ],
    "keywords": [
      "euclidean thurston maps",
      "rationality",
      "computer program netmap",
      "natural geometric quantity",
      "natural notion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}