{
  "id": "1706.05618",
  "version": "v1",
  "published": "2017-06-18T08:18:56.000Z",
  "updated": "2017-06-18T08:18:56.000Z",
  "title": "Persistence of invariant tori in integrable Hamiltonian systems under almost periodic perturbations",
  "authors": [
    "Peng Huang",
    "Xiong Li"
  ],
  "comment": "33 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "In this paper we are concerned with the existence of invariant tori in nearly integrable Hamiltonian systems \\begin{equation*} H=h(y)+f(x,y,t), \\end{equation*} where $y\\in D\\subseteq\\mathbb{R}^n$ with $D$ being a closed bounded domain, $x\\in \\mathbb{T}^n$, $f(x,y,t)$ is a real analytic almost periodic function in $t$ with the frequency ${{\\omega}}=(\\cdots,{{\\omega}}_\\lambda,\\cdots)_{\\lambda\\in \\mathbb{Z}}\\in \\mathbb{R}^{\\mathbb{Z}}$. As an application, we will prove the existence of almost periodic solutions and the boundedness of all solutions for the second order differential equations with superquadratic potentials depending almost periodically on time.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-06-18T08:18:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "integrable hamiltonian systems",
      "invariant tori",
      "periodic perturbations",
      "second order differential equations",
      "persistence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}