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An extension of quantitative nondivergence and applications to Diophantine exponents

Author(s): Dmitry Kleinbock
Journal: Trans. Amer. Math. Soc. 360 (2008), 6497-6523.
MSC (2000): Primary 37A17; Secondary 11J83
Posted: June 26, 2008
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Abstract | References | Similar articles | Additional information

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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Additional Information:

Dmitry Kleinbock
Affiliation: Department of Mathematics, Brandeis University, Waltham, Massachusetts 02454-9110
Email: kleinboc@brandeis.edu

DOI: 10.1090/S0002-9947-08-04592-3
PII: S 0002-9947(08)04592-3
Received by editor(s): December 15, 2006
Posted: June 26, 2008
Additional Notes: This work was supported in part by NSF Grant DMS-0239463.
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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