Measure preserving diffeomorphisms of the torus are unclassifiable

被引：3

作者：

Foreman, Matthew ^{[1
]}

Weiss, Benjamin ^{[2
]}

机构：

[1] Univ Calif Irvine, Dept Math, Irvine, CA 92697 USA

[2] Hebrew Univ Jerusalem, Einstein Inst Math, Edmond J Safra Campus, IL-91904 Jerusalem, Israel

来源：

JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY | 2022年 / 24卷 / 08期

基金：

美国国家科学基金会;

关键词：

Classification of ergodic transformations; odometers; circular systems; distal transformations; Anosov-Katok method; OPERATOR METHODS;

D O I：

10.4171/JEMS/1151

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In 1932 von Neumann proposed classifying the statistical behavior of differentiable systems. In modern language this is interpreted as classifying diffeomorphisms of compact manifolds up to measure isomorphism. This paper proves that this is impossible in a rigorous sense.

引用

页码：2605 / 2690

页数：86

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