{
  "id": "1411.2945",
  "version": "v1",
  "published": "2014-11-11T20:03:56.000Z",
  "updated": "2014-11-11T20:03:56.000Z",
  "title": "Parabolic curves of diffeomorphisms asymptotic to formal invariant curves",
  "authors": [
    "Lorena López-Hernanz",
    "Fernando Sanz Sánchez"
  ],
  "categories": [
    "math.DS",
    "math.CV"
  ],
  "abstract": "We prove that if $F$ is a tangent to the identity diffeomorphism at $0\\in\\mathbb{C}^2$ and $\\Gamma$ is a formal invariant curve of $F$ then there exists a parabolic curve (attracting or repelling) of $F$ asymptotic to $\\Gamma$. The result is a consequence of a more general one in arbitrary dimension, where we prove the existence of parabolic curves of a tangent to the identity diffeomorphism $F$ at $0\\in\\mathbb{C}^n$ asymptotic to a given formal invariant curve under some additional conditions, expressed in terms of a reduction of $F$ to a special normal form by means of blow-ups and ramifications along the formal curve.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-11T20:03:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "formal invariant curve",
      "parabolic curve",
      "diffeomorphisms asymptotic",
      "identity diffeomorphism",
      "special normal form"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1411.2945L"
    }
  }
}