{
  "id": "1303.3099",
  "version": "v1",
  "published": "2013-03-13T07:08:53.000Z",
  "updated": "2013-03-13T07:08:53.000Z",
  "title": "Transitive cylinder flows whose set of discrete points is of full Hausdorff dimension",
  "authors": [
    "Eugeniusz Dymek"
  ],
  "comment": "14 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "For each irrational $\\alpha\\in[0,1)$ we construct a continuous function $f\\: [0,1)\\to \\R$ such that the corresponding cylindrical transformation $[0,1)\\times\\R \\ni (x,t) \\mapsto (x+\\alpha, t+ f(x)) \\in [0,1)\\times\\R$ is transitive and the Hausdorff dimension of the set of points whose orbits are discrete is 2. Such cylindrical transformations are shown to display a certain chaotic behaviour of Devaney-like type.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-03-13T07:08:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B05",
      "37C45",
      "37C29"
    ],
    "keywords": [
      "full hausdorff dimension",
      "transitive cylinder flows",
      "discrete points",
      "chaotic behaviour",
      "corresponding cylindrical transformation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1303.3099D"
    }
  }
}