KAKUTANI EQUIVALENCE OF UNIPOTENT FLOWS

被引：5

作者：

Kanigowski, Adam ^{[1
]}

Vinhage, Kurt ^{[2
]}

Wei, Daren ^{[2
,3
]}

机构：

[1] Univ Maryland, Dept Math, College Pk, MD 20742 USA

[2] Penn State Univ, Dept Math, University Pk, PA 16802 USA

[3] Hebrew Univ Jerusalem, Einstein Inst Math, Jerusalem, Israel

来源：

DUKE MATHEMATICAL JOURNAL | 2021年 / 170卷 / 07期

基金：

美国国家科学基金会;

关键词：

Kakutani equivalence; unipotent flows; loosely Kronecker; homogeneous dynamics; 37A35; 37A20; SLOW ENTROPY; SUBGROUPS;

D O I：

10.1215/00127094-2020-0074

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study Kakutani equivalence in the class of unipotent flows acting on finite-volume quotients of semisimple Lie groups. For every such flow, we compute the Kakutani invariant of M. Ratner, the value being explicitly given by the Jordan block structure of the unipotent element generating the flow. This, in particular, answers a question of M. Ratner. Moreover, it follows that the only loosely Kronecker unipotent flows are given by ((1)(0 1) (t)) x id acting on (SL.(2, R) x G')/Gamma', where Gamma' is an irreducible lattice in SL(2, R) x G' (with the possibility that G' = {e}).

引用

页码：1517 / 1583

页数：67

共 34 条

[1]

ABRAMOV LM, 1959, DOKL AKAD NAUK SSSR+, V128, P647

[2] The complexity of the collection of measure-distal transformations [J].