{
  "id": "0809.1614",
  "version": "v1",
  "published": "2008-09-09T17:29:53.000Z",
  "updated": "2008-09-09T17:29:53.000Z",
  "title": "Unique resonant normal forms for area preserving maps at an elliptic fixed point",
  "authors": [
    "V. Gelfreich",
    "N. Gelfreikh"
  ],
  "comment": "37 pages, 5 figures",
  "doi": "10.1088/0951-7715/22/4/006",
  "categories": [
    "math.DS"
  ],
  "abstract": "We construct a resonant normal form for an area-preserving map near a generic resonant elliptic fixed point. The normal form is obtained by a simplification of a formal interpolating Hamiltonian. The resonant normal form is unique and therefore provides the formal local classification for area-preserving maps with the elliptic fixed point. The total number of formal invariants is infinite. We consider the cases of weak (of order $n\\ge5$) and strong (of order $n=3,4$) resonances. We also construct unique normal forms for analytic families of area-preserving maps. We note that our constructions involve non-linear grading functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-09-09T17:29:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37J40",
      "37G05",
      "70K45",
      "70K42"
    ],
    "keywords": [
      "unique resonant normal forms",
      "area preserving maps",
      "area-preserving map",
      "construct unique normal forms",
      "generic resonant elliptic fixed point"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Nonlinearity",
      "year": 2009,
      "month": "Apr",
      "volume": 22,
      "number": 4,
      "pages": 783
    },
    "note": {
      "typesetting": "TeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009Nonli..22..783G"
    }
  }
}