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Lyapunov spectrum, Harder--Narasimhan filtration and thin monodromy
Abstract
We study the equality case of the inequalities between the Lyapunov spectrum and the Harder--Narasimhan slopes of a semi-simple local system with non-expanding cusp monodromy over a finite-area hyperbolic surface. This gives a nonlattice-transversality alternative of the monodromy group. On the other hand, we generalize Filip's Assumptions A and B to give classes of polarized variation of Hodge structures that achieve the equality. As an application, we recover the thinness of C-32 in Sp6ℝ. Besides, we provide an upper bound, called average Cartan spectrum, that dominates the Lyapunov spectrum and study its rigidity.
Related
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BibTeX
@misc{yu2026lyapunov,
title = {{Lyapunov spectrum, Harder--Narasimhan filtration and thin monodromy}},
author = {Fei Yu and Junming Zhang},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.06388},
eprint = {2611.06388},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.06388},
}
RIS
TY - UNPB
TI - Lyapunov spectrum, Harder--Narasimhan filtration and thin monodromy
AU - Fei Yu
AU - Junming Zhang
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.06388
UR - https://arxiv.org/abs/2611.06388
AB - We study the equality case of the inequalities between the Lyapunov spectrum and the Harder--Narasimhan slopes of a semi-simple local system with non-expanding cusp monodromy over a finite-area hyperbolic surface. This gives a nonlattice-transversality alternative of the monodromy group. On the other hand, we generalize Filip's Assumptions A and B to give classes of polarized variation of Hodge structures that achieve the equality. As an application, we recover the thinness of C-32 in Sp_6ℝ. Besides, we provide an upper bound, called average Cartan spectrum, that dominates the Lyapunov spectrum and study its rigidity.
ER -