{
  "id": "math/0606205",
  "version": "v1",
  "published": "2006-06-09T04:53:59.000Z",
  "updated": "2006-06-09T04:53:59.000Z",
  "title": "Attractor-repeller pair, Morse decomposition and Lyapunov function for random dynamical systems",
  "authors": [
    "Zhenxin Liu",
    "Shuguan Ji",
    "Menglong Su"
  ],
  "comment": "17 pages, Latex",
  "categories": [
    "math.DS"
  ],
  "abstract": "In the stability theory of dynamical systems, Lyapunov functions play a fundamental role. In this paper, we study the attractor-repeller pair decomposition and Morse decomposition for compact metric space in the random setting. In contrast to [8], by introducing slightly stronger definitions of random attractor and repeller, we characterize attractor-repeller pair decompositions and Morse decompositions for random dynamical systems through the existence of Lyapunov functions. These characterizations, we think, deserve to be known widely.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-06-09T04:53:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37H99",
      "37B25",
      "37B55"
    ],
    "keywords": [
      "random dynamical systems",
      "morse decomposition",
      "characterize attractor-repeller pair decompositions",
      "compact metric space",
      "lyapunov functions play"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......6205L"
    }
  }
}