{
  "id": "1803.01954",
  "version": "v1",
  "published": "2018-03-05T22:53:44.000Z",
  "updated": "2018-03-05T22:53:44.000Z",
  "title": "Characteristic directions of two-dimensional biholomorphisms",
  "authors": [
    "Lorena López-Hernanz",
    "Rudy Rosas"
  ],
  "categories": [
    "math.DS",
    "math.CV"
  ],
  "abstract": "We prove that for each characteristic direction $[v]$ of a tangent to the identity diffeomorphism of order $k+1$ in $\\mathbb{C}^2$ there exist either an analytic curve of fixed points tangent to $[v]$ or $k$ parabolic manifolds where all the orbits are tangent to $[v]$, and that at least one of these parabolic manifolds is or contains a parabolic curve.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-03-05T22:53:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "characteristic direction",
      "two-dimensional biholomorphisms",
      "parabolic manifolds",
      "parabolic curve",
      "identity diffeomorphism"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}