{
  "id": "1801.02921",
  "version": "v1",
  "published": "2018-01-09T12:48:47.000Z",
  "updated": "2018-01-09T12:48:47.000Z",
  "title": "The genericity of Arnold diffusion in nearly integrable Hamiltonian systems",
  "authors": [
    "Chong-Qing Cheng"
  ],
  "comment": "to appear",
  "journal": "Asian Journal of Mathematics, 2018",
  "categories": [
    "math.DS"
  ],
  "abstract": "In this paper, we prove that the net of transition chain is $\\delta$-dense for nearly integrable positive definite Hamiltonian systems with 3 degrees of freedom in the cusp-residual generic sense in $C^r$-topology, $r\\ge 6$. The main ingredients of the proof existed in \\cite{CZ,C17a,C17b}. As an immediate consequence, Arnold diffusion exists among this class of Hamiltonian systems. The question of \\cite{C17c} is answered in Section 9 of the paper.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-09T12:48:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "integrable hamiltonian systems",
      "arnold diffusion",
      "genericity",
      "cusp-residual generic sense",
      "integrable positive definite hamiltonian systems"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}