{
  "id": "1112.0370",
  "version": "v3",
  "published": "2011-12-02T01:47:48.000Z",
  "updated": "2012-08-25T17:05:55.000Z",
  "title": "Lyapunov spectrum of invariant subbundles of the Hodge bundle",
  "authors": [
    "Giovanni Forni",
    "Carlos Matheus",
    "Anton Zorich"
  ],
  "comment": "67 pages, 2 figures. New version based on the reports of the referees. To appear in ETDS",
  "journal": "Ergodic Theory and Dynamical Systems, 34:2 (2014), 353-408",
  "doi": "10.1017/etds.2012.148",
  "categories": [
    "math.DS"
  ],
  "abstract": "We study the Lyapunov spectrum of the Kontsevich--Zorich cocycle on $SL(2,\\mathbb{R})$-invariant subbundles of the Hodge bundle over the support of a $SL(2,\\mathbb{R})$-invariant probability measure on the moduli space of Abelian differentials. In particular, we prove formulas for partial sums of Lyapunov exponents in terms of the second fundamental form (or Kodaira--Spencer map) of the Hodge bundle with respect to Gauss--Manin connection and investigate the relations between the central {Oseldets} subbundle and the kernel of the second fundamental form. We illustrate our conclusions in two special cases.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-08-25T17:05:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37Axx"
    ],
    "keywords": [
      "hodge bundle",
      "invariant subbundles",
      "lyapunov spectrum",
      "second fundamental form",
      "invariant probability measure"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 67,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1112.0370F"
    }
  }
}