An extension of quantitative nondivergence and applications to Diophantine exponents

Kleinbock, Dmitry

doi:10.1090/S0002-9947-08-04592-3

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ISSN 1088-6850(online) ISSN 0002-9947(print)

An extension of quantitative nondivergence and applications to Diophantine exponents

Author: Dmitry Kleinbock
Journal: Trans. Amer. Math. Soc. 360 (2008), 6497-6523
MSC (2000): Primary 37A17; Secondary 11J83
Posted: June 26, 2008
MathSciNet review: 2434296
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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 $\mathbb{R}^{n}$ and their nondegenerate submanifolds.

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