{
  "id": "2004.04027",
  "version": "v1",
  "published": "2020-04-08T14:56:29.000Z",
  "updated": "2020-04-08T14:56:29.000Z",
  "title": "Tremors and horocycle dynamics on the moduli space of translation surfaces",
  "authors": [
    "Jon Chaika",
    "John Smillie",
    "Barak Weiss"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We introduce a \"tremor\" deformation on strata of translation surfaces. Using it, we give new examples of behaviors of horocycle flow orbits in strata of translation surfaces. In the genus two stratum with two singular points, we find orbits which are generic for a measure whose support is strictly contained in the orbit and find orbits which are not generic for any measure. We also describe a horocycle orbit-closure whose Hausdorff dimension is not an integer.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-08T14:56:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "translation surfaces",
      "horocycle dynamics",
      "moduli space",
      "horocycle flow orbits",
      "hausdorff dimension"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}