Lyapunov Exponents of variations of Hodge structures with $G_2$ monodromy
Genival da Silva Jr
TL;DR
This paper studies the Lyapunov exponents associated with variations of Hodge structures having $G_2$ monodromy, providing formulas for their sums across different weights.
Contribution
It introduces formulas for the sum of positive Lyapunov exponents in variations of Hodge structures with arbitrary weight and explores the case with $G_2$ monodromy.
Findings
Formulas for sum of positive Lyapunov exponents
Analysis of $G_2$ monodromy in Hodge structures
Insights into Lyapunov spectrum for specific monodromy groups
Abstract
We investigate the Lyapunov Exponents of a variation of Hodge structure which has as geometric monodromy group, and discuss formulas for the sum of positive Lyapunov Exponents of variations of Hodge structures of any weight.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Mathematical Dynamics and Fractals