{
  "id": "math/0503223",
  "version": "v1",
  "published": "2005-03-11T17:14:23.000Z",
  "updated": "2005-03-11T17:14:23.000Z",
  "title": "Area-Preserving Surface Diffeomorphisms",
  "authors": [
    "Zhihong Xia"
  ],
  "doi": "10.1007/s00220-005-1514-3",
  "categories": [
    "math.DS",
    "math.GN"
  ],
  "abstract": "We prove some generic properties for $C^r$, $r=1, 2, ..., \\infty$, area-preserving diffeomorphism on compact surfaces. The main result is that the union of the stable (or unstable) manifolds of hyperbolic periodic points are dense in the surface. This extends the result of Franks and Le Calvez \\cite{FL03} on $S^2$ to general surfaces. The proof uses the theory of prime ends and Lefschetz fixed point theorem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-03-11T17:14:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37J45",
      "37J10"
    ],
    "keywords": [
      "area-preserving surface diffeomorphisms",
      "hyperbolic periodic points",
      "lefschetz fixed point theorem",
      "prime ends",
      "main result"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer",
      "journal": "Commun. Math. Phys."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}