Non-divergence in the space of lattices (Q6062653)

\textit{G. A. Margulis} [Proc. Summer Sch. Bolyai Janos math. Soc., Budapest 1971, 365--370 (1975; Zbl 0305.22014)] introduced the non-divergence property in the context of unipotent flows on the space of lattices of \(\mathbb{R}^n\). Quantitative estimates of this sort were later found by \textit{D. Y. Kleinbock} and \textit{G. A. Margulis} [Ann. Math. (2) 148, No. 1, 339--360 (1998; Zbl 0922.11061)] and used to study problems in Diophantine approximation on manifolds. Here a novel approach is used to give a new formulation and proof of this quantitative non-divergence result by using the Grayson polygon of a lattice and the associated Harder-Narasimhan filtration.