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

Abstract

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.

arXiv comment22 pages, 4 figures; accepted version to be published in Ann. Inst. Fourier (Grenoble)