{
  "id": "1801.09014",
  "version": "v1",
  "published": "2018-01-27T00:48:09.000Z",
  "updated": "2018-01-27T00:48:09.000Z",
  "title": "Poincaré-Bendixson Theorem for Hybrid Systems",
  "authors": [
    "William Clark",
    "Anthony Bloch",
    "Leonardo Colombo"
  ],
  "comment": "Comments welcome",
  "categories": [
    "math.DS",
    "cs.SY",
    "math.OC",
    "nlin.CD"
  ],
  "abstract": "The Poincar\\'e-Bendixson theorem plays an important role in the study of the qualitative behavior of dynamical systems on the plane; it describes the structure of limit sets in such systems. We prove a version of the Poincar\\'e-Bendixson Theorem for two dimensional hybrid dynamical systems and describe a method for computing the derivative of the Poincar\\'e return map, a useful object for the stability analysis of hybrid systems. We also prove a Poincar\\'e-Bendixson Theorem for a class of one dimensional hybrid dynamical systems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-27T00:48:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34A38",
      "34C25",
      "34D20",
      "70K05",
      "70K20",
      "70K42"
    ],
    "keywords": [
      "hybrid systems",
      "poincaré-bendixson theorem",
      "dimensional hybrid dynamical systems",
      "poincare return map",
      "poincare-bendixson theorem plays"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}