Lyapunov Exponents of Rank 2-Variations of Hodge Structures and Modular Embeddings
Annales de l'Institut Fourier, Volume 64 (2014) no. 5, p. 2037-2066

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.

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.

DOI : https://doi.org/10.5802/aif.2903
Classification:  32G20,  37D25,  30F35
Keywords: Lyapunov exponent, Kontsevich-Zorich cocycle, variations of Hodge structures
@article{AIF_2014__64_5_2037_0,
     author = {Kappes, Andr\'e},
     title = {Lyapunov Exponents of Rank $2$-Variations of Hodge Structures and Modular Embeddings},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {64},
     number = {5},
     year = {2014},
     pages = {2037-2066},
     doi = {10.5802/aif.2903},
     zbl = {1314.32020},
     mrnumber = {3330930},
     zbl = {06387330},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2014__64_5_2037_0}
}
Kappes, André. Lyapunov Exponents of Rank $2$-Variations of Hodge Structures and Modular Embeddings. Annales de l'Institut Fourier, Volume 64 (2014) no. 5, pp. 2037-2066. doi : 10.5802/aif.2903. http://www.numdam.org/item/AIF_2014__64_5_2037_0/

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