{
  "id": "0912.2922",
  "version": "v1",
  "published": "2009-12-15T15:22:33.000Z",
  "updated": "2009-12-15T15:22:33.000Z",
  "title": "Unique normal forms for area preserving maps near a fixed point with neutral multipliers",
  "authors": [
    "V. Gelfreich",
    "N. Gelfreikh"
  ],
  "comment": "25 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "We study normal forms for families of area-preserving maps which have a fixed point with neutral multipliers -1 or +1 at epsilon=0. Our study covers both the orientation-preserving and orientation-reversing cases. In these cases Birkhoff normal forms do not provide a substantial simplification of the system. In the paper we prove that the Takens normal form vector field can be substantially simplified. We also show that if certain non-degeneracy conditions are satisfied no further simplification is generically possible since the constructed normal forms are unique. In particular, we provide a full system of formal invariants with respect to formal coordinate changes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-12-15T15:22:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37J40",
      "37G05",
      "70K45",
      "70K42"
    ],
    "keywords": [
      "unique normal forms",
      "area preserving maps",
      "neutral multipliers",
      "fixed point",
      "takens normal form vector field"
    ],
    "publication": {
      "doi": "10.1134/S1560354710020164",
      "journal": "Regular and Chaotic Dynamics",
      "year": 2010,
      "month": "Jun",
      "volume": 15,
      "number": "2-3",
      "pages": 300
    },
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010RCD....15..300G"
    }
  }
}