{
  "id": "2108.07434",
  "version": "v1",
  "published": "2021-08-17T04:08:15.000Z",
  "updated": "2021-08-17T04:08:15.000Z",
  "title": "Poincaré-Hopf theorem for hybrid systems",
  "authors": [
    "Matthew D. Kvalheim"
  ],
  "comment": "6 pages, 1 figure, comments welcome. This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible",
  "categories": [
    "math.DS",
    "cs.RO",
    "math.AT"
  ],
  "abstract": "A generalization of the Poincar\\'{e}-Hopf index theorem applicable to hybrid dynamical systems is obtained. For the hybrid systems considered, guard sets are not assumed to be smooth; distinct \"modes\" are not assumed to have constant dimension; and resets are arbitrary multivalued maps (relations).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-17T04:08:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37C25",
      "47H10",
      "34A38",
      "93C30"
    ],
    "keywords": [
      "hybrid systems",
      "poincaré-hopf theorem",
      "arbitrary multivalued maps",
      "constant dimension",
      "guard sets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}