{
  "id": "2109.08785",
  "version": "v1",
  "published": "2021-09-17T23:41:58.000Z",
  "updated": "2021-09-17T23:41:58.000Z",
  "title": "Quantitative destruction of invariant circles",
  "authors": [
    "Lin Wang"
  ],
  "comment": "arXiv admin note: substantial text overlap with arXiv:1208.2840, arXiv:1403.0986, arXiv:1106.6137",
  "categories": [
    "math.DS"
  ],
  "abstract": "For area-preserving twist maps on the annulus, we consider the problem on quantitative destruction of invariant circles with a given frequency $\\omega$ of an integrable system by a trigonometric polynomial of degree $N$ perturbation $R_N$ with $\\|R_N\\|_{C^r}<\\epsilon$. We obtain a relation among $N$, $r$, $\\epsilon$ and the arithmetic property of $\\omega$, for which the area-preserving map admit no invariant circles with $\\omega$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-09-17T23:41:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "invariant circles",
      "quantitative destruction",
      "area-preserving twist maps",
      "trigonometric polynomial",
      "arithmetic property"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}