紧族与保测作用的典型熵不变量
动力系统
2021-02-12 v1
摘要
对于一个紧的作用集合，选取一个 Kushnirenko 熵型的不变量，使得它在该集合上等于零，但对典型作用为无穷。作为推论，我们证明典型的保测变换不同构于几何形状交换变换。该问题源于 Chaika 和 Davis 关于 IET 的非典型性的结果。
引用
@article{arxiv.2102.06187,
title = {Compact families and typical entropy invariants of measure-preserving actions},
author = {Valery V. Ryzhikov},
journal= {arXiv preprint arXiv:2102.06187},
year = {2021}
}
备注
in Russian. The article is intended for Volume 82:1 of Proceedings of the Moscow Mathematical Society, dedicated to the 80th anniversaries of V.I. Oseledets and A.M. Stepin and the memory of A.M. Stepin, who left us in November 2020