{
  "id": "1808.03596",
  "version": "v1",
  "published": "2018-08-10T15:52:50.000Z",
  "updated": "2018-08-10T15:52:50.000Z",
  "title": "Integrable Hamiltonian systems with a periodic orbit or invariant torus unique in the whole phase space",
  "authors": [
    "Mikhail B. Sevryuk"
  ],
  "comment": "8 pages, submitted to the Arnold Mathematical Journal",
  "categories": [
    "math.DS"
  ],
  "abstract": "It is very well known that periodic orbits of autonomous Hamiltonian systems are generically organized into smooth one-parameter families (the parameter being just the energy value). We present a simple example of an integrable Hamiltonian system (with an arbitrary number of degrees of freedom greater than one) with a unique periodic orbit in the phase space (which is not compact). Similar examples are given for Hamiltonian systems with a unique invariant torus (of any prescribed dimension) carrying conditionally periodic motions. Parallel examples for Hamiltonian systems with a compact phase space and with uniqueness replaced by isolatedness are also constructed. Finally, reversible analogues of all the examples are described.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-10T15:52:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37J45",
      "70H12",
      "70K42",
      "70K43",
      "70H33"
    ],
    "keywords": [
      "integrable hamiltonian system",
      "invariant torus unique",
      "smooth one-parameter families",
      "compact phase space",
      "unique invariant torus"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}