{
  "id": "1207.4016",
  "version": "v2",
  "published": "2012-07-17T14:42:42.000Z",
  "updated": "2013-03-19T10:19:53.000Z",
  "title": "Arnold diffusion in nearly integrable Hamiltonian systems",
  "authors": [
    "Chong-Qing Cheng"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "In this paper, Arnold diffusion is proved to be generic phenomenon in nearly integrable convex Hamiltonian systems with three degrees of freedom: $$ H(x,y)=h(y)+\\epsilon P(x,y), \\qquad x\\in\\mathbb{T}^3,\\ y\\in\\mathbb{R}^3. $$ Under typical perturbation $\\epsilon P$, the system admits \"connecting\" orbit that passes through any two prescribed small balls in the same energy level $H^{-1}(E)$ provided $E$ is bigger than the minimum of the average action, namely, $E>\\min\\alpha$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-03-19T10:19:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "integrable hamiltonian systems",
      "arnold diffusion",
      "integrable convex hamiltonian systems",
      "generic phenomenon",
      "system admits"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1207.4016C"
    }
  }
}