{
  "id": "1808.02691",
  "version": "v1",
  "published": "2018-08-08T09:36:05.000Z",
  "updated": "2018-08-08T09:36:05.000Z",
  "title": "On a matrix-valued PDE characterizing a contraction metric for a periodic orbit",
  "authors": [
    "Peter Giesl"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "The stability and the basin of attraction of a periodic orbit can be determined using a contraction metric, i.e., a Riemannian metric with respect to which adjacent solutions contract. A contraction metric does not require knowledge of the position of the periodic orbit and is robust to perturbations. In this paper we characterize such a Riemannian contraction metric as matrix-valued solution of a linear first-order Partial Differential Equation. This will enable the explicit construction of a contraction metric by numerically solving this equation in future work. In this paper we prove existence and uniqueness of the solution of the PDE and show that it defines a contraction metric.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-08T09:36:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34C25",
      "34D20",
      "37C27"
    ],
    "keywords": [
      "periodic orbit",
      "matrix-valued pde characterizing",
      "linear first-order partial differential equation",
      "riemannian contraction metric",
      "adjacent solutions contract"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}