Exponential mixing of nilmanifold automorphisms

被引：16

作者：

Gorodnik, Alexander ^{[1
]}

Spatzier, Ralf ^{[2
]}

机构：

[1] Univ Bristol, Dept Math, Bristol BS8 1TW, Avon, England

[2] Univ Michigan, Dept Math, Ann Arbor, MI 48109 USA

来源：

JOURNAL D ANALYSE MATHEMATIQUE | 2014年 / 123卷

基金：

英国工程与自然科学研究理事会;

关键词：

PERIODIC POINTS; LIMIT-THEOREMS; FLOWS; TORI;

D O I：

10.1007/s11854-014-0024-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study dynamical properties of automorphisms of compact nilmanifolds and prove that every ergodic automorphism is exponentially mixing and exponentially mixing of higher orders. This allows us to establish probabilistic limit theorems and regularity of solutions of the cohomological equation for such automorphisms. Our method is based on the quantitative equidistribution results for polynomial maps combined with Diophantine estimates.

引用

页码：355 / 396

页数：42

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