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Flows on $S$-arithmetic homogeneous spaces and applications to metric Diophantine approximation

Dmitry Kleinbock·George Tomanov
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Abstract

The main goal of this work is to establish quantitative nondivergence estimates for flows on homogeneous spaces of products of real and $p$-adic Lie groups. These results have applications both to ergodic theory and to Diophantine approximation. Namely, earlier results of Dani (finiteness of locally finite ergodic unipotent-invariant measures on real homogeneous spaces) and Kleinbock-Margulis (strong extremality of nondegenerate submanifolds of $\Bbb R^n$) are generalized to the $S$-arithmetic setting.

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BibTeXRIS

Dmitry Kleinbock, George Tomanov. 2005-06-24. Flows on $S$-arithmetic homogeneous spaces and applications to metric Diophantine approximation. https://arxiv.org/abs/math/0506510

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