{
  "id": "1109.1780",
  "version": "v1",
  "published": "2011-09-08T17:25:20.000Z",
  "updated": "2011-09-08T17:25:20.000Z",
  "title": "Dimension Reduction Near Periodic Orbits of Hybrid Systems",
  "authors": [
    "Samuel Burden",
    "Shai Revzen",
    "S. Shankar Sastry"
  ],
  "comment": "Full version of conference paper appearing in IEEE CDC/ECC 2011",
  "categories": [
    "math.DS",
    "math.DG",
    "nlin.CD"
  ],
  "abstract": "When the Poincar\\'{e} map associated with a periodic orbit of a hybrid dynamical system has constant-rank iterates, we demonstrate the existence of a constant-dimensional invariant subsystem near the orbit which attracts all nearby trajectories in finite time. This result shows that the long-term behavior of a hybrid model with a large number of degrees-of-freedom may be governed by a low-dimensional smooth dynamical system. The appearance of such simplified models enables the translation of analytical tools from smooth systems-such as Floquet theory-to the hybrid setting and provides a bridge between the efforts of biologists and engineers studying legged locomotion.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-09-08T17:25:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "periodic orbit",
      "hybrid systems",
      "dimension reduction",
      "low-dimensional smooth dynamical system",
      "constant-dimensional invariant subsystem"
    ],
    "tags": [
      "conference paper"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1109.1780B"
    }
  }
}