Lyapunov spectrum of invariant subbundles of the Hodge bundle

Details Lyapunov spectrum of invariant subbundles of the Hodge bundle Lyapunov spectrum of invariant subbundles of the Hodge bundle

2011-12-02

arxiv.org/abs/1112.0370v2

Mathematics

Dynamical Systems

63 pages, no figures. Subsections 2.4, 2.5 and the arguments around Theorems 1 and 3 were rewritten (to provide more details)

Scientific paper

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.

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