{
  "id": "math/0412158",
  "version": "v1",
  "published": "2004-12-08T12:46:23.000Z",
  "updated": "2004-12-08T12:46:23.000Z",
  "title": "Dynamics of infinite-multivalued transformations",
  "authors": [
    "Konstantin Igudesman"
  ],
  "comment": "16 pages, latex",
  "categories": [
    "math.DS"
  ],
  "abstract": "We consider a transformation of a normalized measure space such that the image of any point is a finite set. We call such transformation $m$-transformation. In this case the orbit of any point looks like a tree. In the study of $m$-transformations we are interested in the properties of the trees. An $m$-transformation generates a stochastic kernel and a new measure. Using these objects, we introduce analogies of some main concept of ergodic theory: ergodicity, Koopman and Frobenius-Perron operators etc. We prove ergodic theorems and consider examples. We also indicate possible applications to fractal geometry and give a generalization of our construction. Some results which have analogies in the classical ergodic theory we are proved using standard methods. Other results have no analogies.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-12-08T12:46:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A05",
      "28D05",
      "28A80"
    ],
    "keywords": [
      "infinite-multivalued transformations",
      "finite set",
      "point looks",
      "transformation generates",
      "stochastic kernel"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math.....12158I"
    }
  }
}