{
  "id": "math/0210473",
  "version": "v2",
  "published": "2002-10-31T07:15:29.000Z",
  "updated": "2003-02-10T09:53:36.000Z",
  "title": "Lyapunov 1-forms for flows",
  "authors": [
    "M. Farber",
    "T. Kappeler",
    "J. Latschev",
    "E. Zehnder"
  ],
  "comment": "27 pages, 3 figures. This revised version incorporates a few minor improvements",
  "categories": [
    "math.DS",
    "math.AT"
  ],
  "abstract": "In this paper we find conditions which guarantee that a given flow $\\Phi$ on a compact metric space $X$ admits a Lyapunov one-form $\\omega$ lying in a prescribed \\v{C}ech cohomology class $\\xi\\in \\check H^1(X;\\R)$. These conditions are formulated in terms of the restriction of $\\xi$ to the chain recurrent set of $\\Phi$. The result of the paper may be viewed as a generalization of a well-known theorem of C. Conley about the existence of Lyapunov functions.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2003-02-10T09:53:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "compact metric space",
      "chain recurrent set",
      "lyapunov functions",
      "lyapunov one-form",
      "conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math.....10473F"
    }
  }
}