{
  "id": "1006.0882",
  "version": "v2",
  "published": "2010-06-04T12:46:48.000Z",
  "updated": "2012-03-26T21:04:05.000Z",
  "title": "Fatou directions along the Julia set for endomorphisms of CP^k",
  "authors": [
    "Romain Dujardin"
  ],
  "comment": "Final, shorter version, to appear in J. Math. Pures Appl",
  "categories": [
    "math.DS",
    "math.CV"
  ],
  "abstract": "Not much is known about the dynamics outside the support of the maximal entropy measure $\\mu$ for holomorphic endomorphisms of $\\mathbb{CP}^k$. In this article we study the structure of the dynamics on the Julia set, which is typically larger than $Supp(\\mu)$. The Julia set is the support of the so-called Green current $T$, so it admits a natural filtration by the supports of the exterior powers of $T$. For $1\\leq q \\leq k$, let $J_q= Supp(T^q)$. We show that for a generic point of $J_q\\setminus J_{q+1}$ there are at least $(k-q)$ \"Fatou directions\" in the tangent space. We also give estimates for the rate of expansion in directions transverse to the Fatou directions.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-03-26T21:04:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "julia set",
      "fatou directions",
      "maximal entropy measure",
      "green current",
      "holomorphic endomorphisms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1006.0882D"
    }
  }
}