{
  "id": "2209.12765",
  "version": "v1",
  "published": "2022-09-26T15:13:28.000Z",
  "updated": "2022-09-26T15:13:28.000Z",
  "title": "Mather $β$-function for ellipses and rigidity",
  "authors": [
    "Michael",
    "Bialy"
  ],
  "categories": [
    "math.DS",
    "math.DG"
  ],
  "abstract": "The goal of the first part of this note is to get an explicit formula for rotation number and Mather $\\beta$-function for ellipse. This is done here with the help of non-standard generating function of billiard problem. In this way the derivation especially simple. In the second part we discuss application of Mather $\\beta$-function to rigidity problem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-09-26T15:13:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "rigidity problem",
      "explicit formula",
      "rotation number",
      "first part",
      "non-standard generating function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}