## An extension of quantitative nondivergence and applications to Diophantine exponents

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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.## References

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## Additional Information

**Dmitry Kleinbock**- Affiliation: Department of Mathematics, Brandeis University, Waltham, Massachusetts 02454-9110
- MR Author ID: 338996
- Email: kleinboc@brandeis.edu
- Received by editor(s): December 15, 2006
- Published electronically: June 26, 2008
- Additional Notes: This work was supported in part by NSF Grant DMS-0239463.
- © Copyright 2008
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc.
**360**(2008), 6497-6523 - MSC (2000): Primary 37A17; Secondary 11J83
- DOI: https://doi.org/10.1090/S0002-9947-08-04592-3
- MathSciNet review: 2434296