{
  "id": "math/0202233",
  "version": "v1",
  "published": "2002-02-22T18:29:08.000Z",
  "updated": "2002-02-22T18:29:08.000Z",
  "title": "Genericity of zero Lyapunov exponents",
  "authors": [
    "Jairo Bochi"
  ],
  "comment": "28 pages, 1 figure. This is a revised, more readable, version of the preprint distributed in 2000",
  "journal": "Ergodic Theory and Dynamical Systems, 22 (2002), 1667-1696",
  "doi": "10.1017/S0143385702001165",
  "categories": [
    "math.DS"
  ],
  "abstract": "We show that, for any compact surface, there is a residual (dense $G_\\delta$) set of $C^1$ area preserving diffeomorphisms which either are Anosov or have zero Lyapunov exponents a.e. This result was announced by R. Mane, but no proof was available. We also show that for any fixed ergodic dynamical system over a compact space, there is a residual set of continuous $SL(2,R)$-cocycles which either are uniformly hyperbolic or have zero exponents a.e.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-02-22T18:29:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37D25",
      "37C20"
    ],
    "keywords": [
      "zero lyapunov exponents",
      "genericity",
      "compact surface",
      "residual set",
      "compact space"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......2233B"
    }
  }
}