On metric Diophantine approximation in matrices and Lie groups

被引：7

作者：

Aka, Menny ^{[1
]}

Breuillard, Emmanuel ^{[2
]}

Rosenzweig, Lior ^{[3
]}

de Saxce, Nicolas ^{[4
]}

机构：

[1] ETH, Dept Math, CH-8092 Zurich, Switzerland

[2] Univ Paris 11, Math Lab, F-91405 Orsay, France

[3] KTH, Dept Math, SE-10044 Stockholm, Sweden

[4] Univ Paris 13, Inst Galilee, LAGA, F-93430 Villetaneuse, France

来源：

COMPTES RENDUS MATHEMATIQUE | 2015年 / 353卷 / 03期

关键词：

HOMOGENEOUS SPACES; DYNAMICS; FLOWS;

D O I：

10.1016/j.crma.2014.12.007

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the Diophantine exponent of analytic submanifolds of m x n real matrices, answering questions of Beresnevich, Kleinbock, and Margulis. We identify a family of algebraic obstructions to the extremality of such a submanifold, and give a formula for the exponent when the submanifold is algebraic and defined over Q. We then apply these results to the determination of the Diophantine exponent of rational nilpotent Lie groups. (C) 2015 Published by Elsevier Masson SAS on behalf of Academie des sciences.

引用

页码：185 / 189

页数：5

共 13 条

[1]

Aka M., 2015, COMPOS MATH

[2]

Aka M., METRIC DIOPHAN UNPUB

[3]

Beresnevich V., J THEOR NOM IN PRESS

[4] On the spectral gap for finitely-generated subgroups of SU(2) [J].