{
  "id": "math/0412335",
  "version": "v2",
  "published": "2004-12-16T21:36:13.000Z",
  "updated": "2005-01-18T14:23:08.000Z",
  "title": "Complexity of piecewise convex transformations in two dimensions, with applications to polygonal billiards",
  "authors": [
    "E. Gutkin",
    "S. Tabachnikov"
  ],
  "comment": "references added, typos corrected",
  "journal": "Moscow Mathematical Journal 6 (2006), 673 -- 701",
  "categories": [
    "math.DS"
  ],
  "abstract": "We introduce the class of piecewise convex transformations, and study their complexity. We apply the results to the complexity of polygonal billiards on surfaces of constant curvature.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-01-18T14:23:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "piecewise convex transformations",
      "polygonal billiards",
      "complexity",
      "applications"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math.....12335G"
    }
  }
}