{
  "id": "1309.7103",
  "version": "v2",
  "published": "2013-09-27T02:50:06.000Z",
  "updated": "2014-11-14T13:34:07.000Z",
  "title": "Degenerations of Complex Dynamical Systems II: Analytic and Algebraic Stability",
  "authors": [
    "Laura DeMarco",
    "Xander Faber"
  ],
  "comment": "Restricted to non-Archimedean fields of residue characteristic zero (a gap in the argument for positive residue characteristic was found in the previous version)",
  "categories": [
    "math.DS"
  ],
  "abstract": "The first article in this series exhibited uniqueness of the weak limit of the equilibrium measures for a degenerating 1-parameter family of rational functions on the Riemann sphere. Here we construct a convergent countable-state Markov chain that computes the limit measure. Our technique is combinatorial in nature and may be applied to compute the location of mass for the equilibrium measure of a non-Archimedean rational function, under a certain stability hypothesis. As a byproduct, we deduce that meromorphic maps preserving the fibers of a rationally-fibered complex surface are algebraically stable after a proper modification.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-09-27T02:50:06.000Z",
      "comment": null,
      "journal": null,
      "doi": null,
      "authors": [
        "Laura De Marco",
        "Xander Faber"
      ]
    },
    {
      "version": "v2",
      "updated": "2014-11-14T13:34:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F10",
      "37P50",
      "37F45"
    ],
    "keywords": [
      "complex dynamical systems",
      "algebraic stability",
      "degenerations",
      "equilibrium measure",
      "convergent countable-state markov chain"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.7103D"
    }
  }
}