{
  "id": "1301.4403",
  "version": "v1",
  "published": "2013-01-18T15:22:01.000Z",
  "updated": "2013-01-18T15:22:01.000Z",
  "title": "Degenerate random perturbations of Anosov diffeomorphisms",
  "authors": [
    "Tatiana Yarmola"
  ],
  "journal": "Ergodic Theory Dynam. Systems 30 (2010), no. 3, 931 to 951",
  "categories": [
    "math.DS"
  ],
  "abstract": "This paper deals with random perturbations of diffeomorphisms on n-dimensional Riemannian manifolds with distributions supported on k-dimensional disks, where k<n. First we demonstrate general but not very intuitive conditions which guarantee that all invariant measures for rank k random perturbations of $C^2$ diffeomorphisms are absolutely continuous with respect to the Riemannian measure on M. For two subclasses of Anosov diffeomorphisms: hyperbolic toral automorphisms and Anosov diffeomorphisms with codimension 1 stable manifolds, the above conditions are modified in order to relate k-dimensional disks that support the distributions to certain foliations that arise from Anosov diffeomorphisms. We conclude that generic rank k random perturbations have absolutely continuous invariant measures.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-01-18T15:22:01.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "anosov diffeomorphisms",
      "degenerate random perturbations",
      "hyperbolic toral automorphisms",
      "relate k-dimensional disks",
      "n-dimensional riemannian manifolds"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1301.4403Y"
    }
  }
}