{
  "id": "0810.4377",
  "version": "v1",
  "published": "2008-10-24T04:23:44.000Z",
  "updated": "2008-10-24T04:23:44.000Z",
  "title": "$\\ell$- Volterra Quadratic Stochastic Operators: Lyapunov Functions, Trajectories",
  "authors": [
    "U. A. Rozikov",
    "A. Zada"
  ],
  "comment": "11 pages",
  "categories": [
    "math.DS",
    "math.FA"
  ],
  "abstract": "We consider $\\ell$-Volterra quadratic stochastic operators defined on $(m-1)$-dimensional simplex, where $\\ell\\in\\{0,1,...,m\\}$. Under some conditions on coefficients of such operators we describe Lyapunov functions and apply them to obtain upper estimates for the set of $\\omega$- limit points of trajectories. We describe a set of fixed points of $\\ell$-Volterra operators.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-10-24T04:23:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60C20"
    ],
    "keywords": [
      "lyapunov functions",
      "trajectories",
      "volterra quadratic stochastic operators",
      "volterra operators",
      "dimensional simplex"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0810.4377R"
    }
  }
}