An extension of quantitative nondivergence and applications to Diophantine exponents

Mathematics – Dynamical Systems

Scientific paper

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26 pages, a revised version. Trans. AMS, to appear

Scientific paper

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.

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