{
  "id": "1611.08490",
  "version": "v1",
  "published": "2016-11-25T15:25:30.000Z",
  "updated": "2016-11-25T15:25:30.000Z",
  "title": "Degeneration of endomorphisms of the complex projective space in the hybrid space",
  "authors": [
    "Charles Favre"
  ],
  "comment": "35 pages",
  "categories": [
    "math.DS",
    "math.CV"
  ],
  "abstract": "Consider a meromorphic familly of endomorphims of degree at least 2 of a complex projective space that is parameterized by the unit disk. We prove that the measure of maximal entropy of these endomorphisms converges to the equilibrium measure of the associated non-Archimedean dynamical system when the system degenerates. The convergence holds in the hybrid space constructed by Boucksom and Jonsson. We also infer from our analysis an estimate for the blow-up of the Lyapunov exponent near a pole in one-dimensional families of endomorphisms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-11-25T15:25:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "complex projective space",
      "hybrid space",
      "degeneration",
      "one-dimensional families",
      "endomorphisms converges"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}