# An extension of quantitative nondivergence and applications to Diophantine exponents

Research paper by Dmitry Kleinbock

Indexed on: 19 May '08Published on: 19 May '08Published in: Mathematics - Dynamical Systems

#### Abstract

We present a sharpening of nondivergence estimates for unipotent (or more generally polynomial-like) flows on homogeneous spaces. Applied to metric Diophantine approximation, it yields precise formulas for Diophantine exponents of affine subspaces of $\Bbb R^n$ and their nondegenerate submanifolds.