{
  "id": "1401.1002",
  "version": "v3",
  "published": "2014-01-06T07:35:36.000Z",
  "updated": "2015-04-16T05:40:30.000Z",
  "title": "Differentiability of Hausdorff dimension of the non-wandering set in a planar open billiard",
  "authors": [
    "Paul Wright"
  ],
  "comment": "25 pages, 0 figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "We consider open billiards in the plane satisfying the no-eclipse condition. We show that the points in the non-wandering set depend differentiably on deformations to the boundary of the billiard. We use Bowen's equation to estimate the Hausdorff dimension of the non-wandering set of the billiard. Finally we show that the Hausdorff dimension depends differentiably on sufficiently smooth deformations to the boundary of the billiard, and estimate the derivative with respect to such deformations.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-01-20T04:10:09.000Z",
      "abstract": "We consider open billiards in the plane satisfying the no-eclipse condition. We show that the points in the non-wandering set depend differentiably on deformations to the boundary of the billiard. We use Bowen's equation to estimate the Hausdorff dimension of the non-wandering set of the billiard, confirming and extending results in [K]. Finally we show that the Hausdorff dimension depends differentiably on sufficiently smooth deformations to the boundary of the billiard, and estimate the derivative with respect to the deformation.",
      "comment": "17 pages, 0 figures",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2015-04-16T05:40:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "planar open billiard",
      "differentiability",
      "no-eclipse condition",
      "non-wandering set depend",
      "sufficiently smooth deformations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1401.1002W"
    }
  }
}