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

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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.
56 pages; an earlier version is available as an MPI (Bonn) preprint, 2003

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Number Theory, Dynamical Systems, 11J83; 37A13

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http://salesiana.dossiersoluciones.com/handle/123456789/75582

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0506510
 http://arxiv.org/abs/math/0506510

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arXiv