Singular vectors on manifolds and fractals

被引：5

作者：

Kleinbock, Dmitry ^{[1
]}

Moshchevitin, Nikolay ^{[2
,3
]}

Weiss, Barak ^{[4
]}

机构：

[1] Brandeis Univ, Dept Math, Waltham, MA 02454 USA

[2] Moscow MV Lomonosov State Univ, Leninskie Gory 1, Moscow 1119991, Russia

[3] Astrakhan State Univ, Tatishcheva 20a, Astrakhan 414056, Russia

[4] Tel Aviv Univ, Dept Math, IL-69978 Tel Aviv, Israel

来源：

ISRAEL JOURNAL OF MATHEMATICS | 2021年 / 245卷 / 02期

基金：

美国国家科学基金会;

关键词：

DIOPHANTINE APPROXIMATION; HOMOGENEOUS SPACES; DIVERGENT TRAJECTORIES; HAUSDORFF DIMENSION; UNIFORM EXPONENTS; REAL NUMBER; FLOWS; THEOREM;

D O I：

10.1007/s11856-021-2220-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We generalize Khintchine's method of constructing totally irrational singular vectors and linear forms. The main result of the paper shows existence of totally irrational vectors and linear forms with large uniform Diophantine exponents on certain subsets of Double-struck capital R-n, in particular on any analytic submanifold of Double-struck capital R-n of dimension >= 2 which is not contained in a proper rational affine subspace.

引用

页码：589 / 613

页数：25

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