{
  "id": "1211.6480",
  "version": "v1",
  "published": "2012-11-27T23:51:05.000Z",
  "updated": "2012-11-27T23:51:05.000Z",
  "title": "Destruction of Lagrangian torus for positive definite Hamiltonian systems",
  "authors": [
    "Chong-Qing Cheng",
    "Lin Wang"
  ],
  "comment": "accepted by Geometric and Functional Analysis (GAFA). arXiv admin note: substantial text overlap with arXiv:1208.2840",
  "categories": [
    "math.DS",
    "math.FA"
  ],
  "abstract": "For an integrable Hamiltonian $H_0=1/2\\sum_{i=1}^dy_i^2$ $(d\\geq 2)$, we show that any Lagrangian torus with a given unique rotation vector can be destructed by arbitrarily $C^{2d-\\delta}$-small perturbations. In contrast with it, it has been shown that KAM torus with constant type frequency persists under $C^{2d+\\delta}$-small perturbations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-11-27T23:51:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "positive definite hamiltonian systems",
      "lagrangian torus",
      "constant type frequency persists",
      "destruction",
      "small perturbations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1211.6480C"
    }
  }
}