{
  "id": "2106.05676",
  "version": "v1",
  "published": "2021-06-10T11:49:55.000Z",
  "updated": "2021-06-10T11:49:55.000Z",
  "title": "Linear Stability of Periodic Trajectories in Inverse Magnetic Billiards",
  "authors": [
    "Sean Gasiorek"
  ],
  "comment": "23 pages, 9 figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "We study the stability of periodic trajectories of planar inverse magnetic billiards, a dynamical system whose trajectories are straight lines inside a connected planar domain $\\Omega$ and circular arcs outside $\\Omega$. Explicit examples are calculated in circles, ellipses, and the one parameter family of curves $x^{2k}+y^{2k}=1$. Comparisons are made to the linear stability of periodic billiard and magnetic billiard trajectories.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-10T11:49:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37J25",
      "37J46",
      "78A35"
    ],
    "keywords": [
      "periodic trajectories",
      "linear stability",
      "planar inverse magnetic billiards",
      "straight lines inside",
      "magnetic billiard trajectories"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}