{
  "id": "2312.01322",
  "version": "v1",
  "published": "2023-12-03T08:58:42.000Z",
  "updated": "2023-12-03T08:58:42.000Z",
  "title": "Weak KAM Theory in Quasi-periodic Hamiltonian Systems",
  "authors": [
    "Xun Niu",
    "Yong Li"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We investigate the dynamics of quasi-periodic Hamiltonian systems from the perspective of weak KAM theory. We obtain that the limit $u$, which obtained from convergence of a sequence of functional minimizers, satisfies Hamilton-Jacobi equations in a weak sense. This is the so-called weak KAM solutions. Meanwhile, we also get a minimal measures $\\mu$.Finally, we discuss the existence and uniqueness of smooth solutions to a kind of divergence equation by the continuation method, which is crucial to our approach.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-12-03T08:58:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "weak kam theory",
      "quasi-periodic hamiltonian systems",
      "satisfies hamilton-jacobi equations",
      "weak kam solutions",
      "continuation method"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}