Flows on S-arithmetic homogeneous spaces and applications to metric Diophantine approximation
Flows on S-arithmetic homogeneous spaces and applications to metric Diophantine approximation
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DOI：
10.4171/cmh/102
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发表时间：
2005-06
影响因子：
0.9
通讯作者：
D. Kleinbock;G. Tomanov
中科院分区：
文献类型：
--
作者：
D. Kleinbock;G. Tomanov
这项工作的主要目标是建立实数李群和 p 进李群乘积的齐次空间上流的定量无散估计。这些结果可应用于遍历理论和丢番图近似。即，Dani（实齐次空间上局部有限遍历单能不变测度的有限性）和 Kleinbock?Margulis（Rn 的非简并子流形的强极值性）的早期结果被推广到 S 算术设置。
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 Rn) are generalized to the S-arithmetic setting.