Lyapunov Exponents of Rank $2$-Variations of Hodge Structures and Modular Embeddings

Kappes, André

Annales de l'Institut Fourier, Tome 64 (2014) no. 5, pp. 2037-2066.

Si la représentation de monodromie d’une variation de structures de Hodge sur une courbe hyperbolique stabilise un sous-espace de rang 2, elle possède un seul exposant de Lyapunov non-negative. Nous deduisons une formule explicite pour cet exposant dans le cas où la monodromie est discrète en employant seulement la représentation.

If the monodromy representation of a VHS over a hyperbolic curve stabilizes a rank two subspace, there is a single non-negative Lyapunov exponent associated with it. We derive an explicit formula using only the representation in the case when the monodromy is discrete.

Classification : 32G20, 37D25, 30F35
Keywords: Lyapunov exponent, Kontsevich-Zorich cocycle, variations of Hodge structures
Mot clés : Exposants de Lyapunov, cocycle de Kontsevich-Zorich, variations de structures de Hodge

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