{
  "id": "2305.15278",
  "version": "v1",
  "published": "2023-05-24T16:03:21.000Z",
  "updated": "2023-05-24T16:03:21.000Z",
  "title": "Dynamics of inner functions revisited",
  "authors": [
    "Jon Aaronson",
    "Mahendra Nadkarni"
  ],
  "comment": "25 pages",
  "categories": [
    "math.DS",
    "math.CV",
    "math.PR"
  ],
  "abstract": "The circle restrictions of inner functions of the unit disc are nonsingular maps of the circle. We study their structure showing that the local invertibility of a restriction is independent of its singularity set. We also study the spectral theory of the transfer operators of a probability preserving inner functions, establishing a spectral gap and some central limit properties of stochastic processes driven by them as a consequence of suitable analytic perturbations of the transfer operators.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-24T16:03:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "30J05",
      "37C30",
      "60F05",
      "28A50"
    ],
    "keywords": [
      "transfer operators",
      "stochastic processes driven",
      "central limit properties",
      "probability preserving inner functions",
      "suitable analytic perturbations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}