{
  "id": "1508.05062",
  "version": "v1",
  "published": "2015-08-20T18:17:10.000Z",
  "updated": "2015-08-20T18:17:10.000Z",
  "title": "A class of adding machine and Julia sets",
  "authors": [
    "Danilo Antonio Caprio"
  ],
  "comment": "22 pages, 8 figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "In this work we define a stochastic adding machine associated to the Fibonacci base and to a probabilities sequence $\\overline{p}=(p_i)_{i\\geq 1}$. We obtain a Markov chain whose states are the set of nonnegative integers. We study probabilistic properties of this chain, such as transience and recurrence. We also prove that the spectrum associated to this Markov chain is connected to the fibered Julia sets for a class of endomorphisms in $\\mathbb{C}^2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-08-20T18:17:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "markov chain",
      "study probabilistic properties",
      "probabilities sequence",
      "stochastic adding machine",
      "fibered julia sets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}