Hausdorff dimension of divergent trajectories on homogeneous spaces

被引：5

作者：

Guan, Lifan ^{[1
,2
]}

Shi, Ronggang ^{[3
]}

机构：

[1] Univ York, Dept Math, York YO10 5DD, N Yorkshire, England

[2] Georg August Univ Gottingen, Math Inst, Bunsenstr 3-5, D-37073 Gottingen, Germany

[3] Fudan Univ, Shanghai Ctr Math Sci, Shanghai 200433, Peoples R China

来源：

COMPOSITIO MATHEMATICA | 2020年 / 156卷 / 02期

基金：

英国工程与自然科学研究理事会;

关键词：

homogeneous dynamics; divergent trajectory; Hausdorff dimension; GEODESICS; PRODUCT; ESCAPE; FLOWS; MASS; SET;

D O I：

10.1112/S0010437X19007711

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For a one-parameter subgroup action on a finite-volume homogeneous space, we consider the set of points admitting divergent-on-average trajectories. We show that the Hausdorff dimension of this set is strictly less than the manifold dimension of the homogeneous space. As a corollary we know that the Hausdorff dimension of the set of points admitting divergent trajectories is not full, which proves a conjecture of Cheung [Hausdorff dimension of the set of singular pairs, Ann. of Math. (2) 173 (2011), 127-167].

引用

页码：340 / 359

页数：20

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