{
  "id": "1312.6154",
  "version": "v1",
  "published": "2013-12-20T21:40:26.000Z",
  "updated": "2013-12-20T21:40:26.000Z",
  "title": "Simplified normal forms near a degenerate elliptic fixed point in two-parametric families of area-preserving maps",
  "authors": [
    "Vassili Gelfreich",
    "Natalia Gelfreikh"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We derive simplified normal forms for an area-preserving map in a neighbourhood of a degenerate resonant elliptic fixed point. Such fixed points appear in generic two-parameter families of area-preserving maps. We also derive a simplified normal form for a generic two-parametric unfolding. The normal forms are used to analyse bifurcations of $n$-periodic orbits. In particular, for $n\\ge6$ we find regions of parameters where the normal form has \"meandering'' invariant curves.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-12-20T21:40:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37J40",
      "37G05",
      "70K45",
      "70K42"
    ],
    "keywords": [
      "simplified normal form",
      "degenerate elliptic fixed point",
      "area-preserving map",
      "two-parametric families",
      "resonant elliptic fixed point"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1088/0951-7715/27/7/1645",
      "journal": "Nonlinearity",
      "year": 2014,
      "month": "Jul",
      "volume": 27,
      "number": 7,
      "pages": 1645
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014Nonli..27.1645G"
    }
  }
}