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We investigate the Lyapunov Exponents of a variation of Hodge structure which has $G_2$ as geometric monodromy group, and discuss formulas for the sum of positive Lyapunov Exponents of variations of Hodge structures of any weight.
The main problem addressed in the paper is the Torelli problem for n-dimensional varieties of general type, more specifically for varieties with ample canonical bundle. It asks under which geometrical condition for a variety the period map for the Ho
We construct a Teichmueller curve uniformized by the Fuchsian triangle group (m,n,infty) for every m<n. Our construction includes the Teichmueller curves constructed by Veech and Ward as special cases. The construction essentially relies on propertie
In this paper we study the $mathbb{C}^*$-fixed points in moduli spaces of Higgs bundles over a compact Riemann surface for a complex semisimple Lie group and its real forms. These fixed points are called Hodge bundles and correspond to complex variat
Lagrangian techniques, such as the finite-time Lyapunov exponent (FTLE) and hyperbolic Lagrangian coherent structures (LCS), have become popular tools for analyzing unsteady fluid flows. These techniques identify regions where particles transported b
In an algebraic family of rational maps of $mathbb{P}^1$, we show that, for almost every parameter for the trace of the bifurcation current of a marked critical value, the critical value is Collet-Eckmann. This extends previous results of Graczyk and