Lyapunov Exponents of Rank 2-Variations of Hodge Structures and Modular Embeddings  [ Exposants de Lyapunov de variations de structures de Hodge de rang 2 et plongements modulaires ]
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.

Reçu le : 2013-03-13
Accepté le : 2013-05-25
DOI : https://doi.org/10.5802/aif.2903
Classification : 32G20,  37D25,  30F35
Mots clés: Exposants de Lyapunov, cocycle de Kontsevich-Zorich, variations de structures de Hodge
@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},
     pages = {2037--2066},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {64},
     number = {5},
     year = {2014},
     doi = {10.5802/aif.2903},
     zbl = {06387330},
     mrnumber = {3330930},
     language = {en},
     url = {aif.centre-mersenne.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, Tome 64 (2014) no. 5, pp. 2037-2066. doi : 10.5802/aif.2903. https://aif.centre-mersenne.org/item/AIF_2014__64_5_2037_0/

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