{
  "id": "1807.07270",
  "version": "v1",
  "published": "2018-07-19T07:40:00.000Z",
  "updated": "2018-07-19T07:40:00.000Z",
  "title": "Singularities of inner functions associated with hyperbolic maps",
  "authors": [
    "Vasiliki Evdoridou",
    "Núria Fagella",
    "Xavier Jarque",
    "David J. Sixsmith"
  ],
  "categories": [
    "math.DS",
    "math.CV"
  ],
  "abstract": "Let $f$ be a function in the Eremenko-Lyubich class $\\mathcal{B}$, and let $U$ be an unbounded, forward invariant Fatou component of $f$. We relate the number of singularities of an inner function associated to $f|_U$ with the number of tracts of $f$. In particular, we show that if $f$ lies in either of two large classes of functions in $\\mathcal{B}$, and also has finitely many tracts, then the number of singularities of an associated inner function is at most equal to the number of tracts of $f$. Our results imply that for hyperbolic functions of finite order there is an upper bound -- related to the order -- on the number of singularities of an associated inner function.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-07-19T07:40:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hyperbolic maps",
      "singularities",
      "associated inner function",
      "forward invariant fatou component",
      "upper bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}