{
  "id": "1808.09911",
  "version": "v1",
  "published": "2018-08-29T16:23:54.000Z",
  "updated": "2018-08-29T16:23:54.000Z",
  "title": "Multi-rotations on the unit circle",
  "authors": [
    "Han Yu"
  ],
  "comment": "A certain number of pages",
  "categories": [
    "math.DS",
    "math.MG"
  ],
  "abstract": "In this paper, we study multi-rotation orbits on the unit circle. We obtain a natural generalization of a classical result which says that orbits of irrational rotations on the unit circle are dense. It is possible to show that this result holds true if instead of iterating a single irrational rotation, one takes a multi-rotation orbit along a finitely recurrent sequence over finitely many different irrational rotations. We also discuss some connections between the box dimensions of multi-rotation orbits and Diophantine approximations. In particular, we improve a result by Feng and Xiong in the case when the rotation parameters are algebraic numbers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-29T16:23:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "28A80",
      "37C45",
      "11B30"
    ],
    "keywords": [
      "unit circle",
      "study multi-rotation orbits",
      "single irrational rotation",
      "result holds true",
      "finitely recurrent sequence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}