{
  "id": "1708.01077",
  "version": "v1",
  "published": "2017-08-03T09:39:41.000Z",
  "updated": "2017-08-03T09:39:41.000Z",
  "title": "Complex rotation numbers: bubbles and their intersections",
  "authors": [
    "Nataliya Goncharuk"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "The construction of complex rotation numbers, due to V.Arnold, gives rise to a fractal-like set \"bubbles\" related to a circle diffeomorphism. \"Bubbles\" is a complex analogue to Arnold tongues. This article contains a survey of the known properties of bubbles, as well as a variety of open questions. In particular, we show that bubbles can intersect and self-intersect, and provide approximate pictures of bubbles for perturbations of M\\\"obius circle diffeomorphisms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-08-03T09:39:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37E10",
      "37E45"
    ],
    "keywords": [
      "complex rotation numbers",
      "intersections",
      "circle diffeomorphism",
      "complex analogue",
      "approximate pictures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}