{
  "id": "2002.08479",
  "version": "v1",
  "published": "2020-02-19T22:24:48.000Z",
  "updated": "2020-02-19T22:24:48.000Z",
  "title": "Periodic orbits of Linear and Invariant flows on Semisimple Lie groups",
  "authors": [
    "S. N. Stelmastchuk"
  ],
  "comment": "7 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "Our main is to study periodic orbits of linear or invariant flows on a real, connected, semisimple Lie group. Since there exist a derivation of Lie algebra to linear or invariant flow, we show that a periodic orbit that is not fixed point of a linear or invariant flow is periodic if and only the eingevalues of derivation is 0 or $\\pm \\alpha i$ for an unique $\\alpha \\neq 0$ and they are semisimple. We apply this result in noncompact case through Iwasawa's decomposition. Furthermore, we present a version of Poincar\\'e-Bendixon's Theorem for periodic orbits.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-19T22:24:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "semisimple lie group",
      "invariant flow",
      "study periodic orbits",
      "derivation",
      "lie algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}