{
  "id": "0704.0949",
  "version": "v1",
  "published": "2007-04-06T21:31:14.000Z",
  "updated": "2007-04-06T21:31:14.000Z",
  "title": "Conservation laws for invariant functionals containing compositions",
  "authors": [
    "Gastao S. F. Frederico",
    "Delfim F. M. Torres"
  ],
  "comment": "Accepted for an oral presentation at the 7th IFAC Symposium on Nonlinear Control Systems (NOLCOS 2007), to be held in Pretoria, South Africa, 22-24 August, 2007",
  "journal": "Applicable Analysis, Volume 86, Issue 9, 2007, pp. 1117-1126.",
  "doi": "10.1080/00036810701584583",
  "categories": [
    "math.OC"
  ],
  "abstract": "The study of problems of the calculus of variations with compositions is a quite recent subject with origin in dynamical systems governed by chaotic maps. Available results are reduced to a generalized Euler-Lagrange equation that contains a new term involving inverse images of the minimizing trajectories. In this work we prove a generalization of the necessary optimality condition of DuBois-Reymond for variational problems with compositions. With the help of the new obtained condition, a Noether-type theorem is proved. An application of our main result is given to a problem appearing in the chaotic setting when one consider maps that are ergodic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-04-06T21:31:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49K05",
      "49J05"
    ],
    "keywords": [
      "invariant functionals containing compositions",
      "conservation laws",
      "necessary optimality condition",
      "generalized euler-lagrange equation",
      "chaotic maps"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0704.0949F"
    }
  }
}