{
  "id": "1505.04477",
  "version": "v1",
  "published": "2015-05-18T00:02:09.000Z",
  "updated": "2015-05-18T00:02:09.000Z",
  "title": "Nonexistence of Lyapunov Exponents for Matrix Cocycles",
  "authors": [
    "Xueting Tian"
  ],
  "comment": "arXiv admin note: substantial text overlap with arXiv:0808.0350 by other authors",
  "categories": [
    "math.DS"
  ],
  "abstract": "It follows from Oseledec Multiplicative Ergodic Theorem that the Lyapunov-irregular set of points for which the Oseledec averages of a given continuous cocycle diverge has zero measure with respect to any invariant probability measure. In strong contrast, for any dynamical system $f:X\\rightarrow X$ with exponential specification property and a H$\\ddot{\\text{o}}$lder continuous matrix cocycle $A:X\\rightarrow G (m,\\mathbb{R})$, we show here that if there exist ergodic measures with different Lyapunov spectrum, then the Lyapunov-irregular set of $A$ is residual (i.e., containing a dense $G_\\delta$ set).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-18T00:02:09.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lyapunov exponents",
      "nonexistence",
      "lyapunov-irregular set",
      "oseledec multiplicative ergodic theorem",
      "invariant probability measure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150504477T"
    }
  }
}