{
  "id": "1703.10785",
  "version": "v1",
  "published": "2017-03-31T08:13:03.000Z",
  "updated": "2017-03-31T08:13:03.000Z",
  "title": "Covariant geometric characterization of slow invariant manifolds: New concepts and viewpoints",
  "authors": [
    "Dirk Lebiedz"
  ],
  "comment": "2 pages, 3 figures, Extended Abstract for IWMRRF 2017",
  "categories": [
    "math.DS",
    "math.DG"
  ],
  "abstract": "We point out a new view on slow invariant manifolds (SIM) in dynamical systems which departs from a purely geometric covariant characterization implying coordinate independency. The fundamental idea is to treat the SIM as a well-defined geometric object in phase space and elucidate characterizing geometric properties that can be evaluated as point-wise analytic criteria. For that purpose, we exploit curvature concepts and formulate our recent variational approach in terms of coordinate-independent Hamiltonian mechanics.Finally, we combine both approaches and conjecture a differential geometric definition of slow invariant manifolds. For the Davis-Skodje model the latter can be completely expatiated.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-31T08:13:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "slow invariant manifolds",
      "covariant geometric characterization",
      "characterization implying coordinate independency",
      "geometric covariant characterization implying coordinate"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 2,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}