{
  "id": "2312.01695",
  "version": "v1",
  "published": "2023-12-04T07:33:38.000Z",
  "updated": "2023-12-04T07:33:38.000Z",
  "title": "Quantitative Destruction of Lagrangian Torus",
  "authors": [
    "Lin Wang"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "Let $P_N$ be a trigonometric polynomial of degree $N$ and satisfy $\\|P_N\\|_{C^r}\\leq \\epsilon$. If $P_N$ destroys the Lagrangian torus with the rotation vector $\\omega$ of an integrable Hamiltonian system, then {what are the relation among $\\epsilon$, $N$, $r$ and the arithmetic property of $\\omega$}? By addressing this, we provide quantitatively higher dimensional generalizations of the remarkable results on destruction of invariant circles for the area-preserving twist map by Herman [21] in 1983 and Mather [28] in 1988.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-12-04T07:33:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lagrangian torus",
      "quantitative destruction",
      "quantitatively higher dimensional generalizations",
      "arithmetic property",
      "area-preserving twist map"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}