Examples in the entropy theory of countable group actions
Examples in the entropy theory of countable group actions
复制标题
DOI：
10.1017/etds.2019.18
复制
发表时间：
2020-10-01
影响因子：
0.9
通讯作者：
Bowen, Lewis
中科院分区：
文献类型：
--
作者：
Bowen, Lewis
Kolmogorov-Sinai熵是整数群的测度保持作用的不变量，是分类理论的核心。有两个最近发展的不变量，sofic熵和Rokhlin熵，推广经典的熵可数群的行动。这些新理论具有违反直觉的性质，例如增加熵的因子映射。这篇综述文章的重点是例子，其中许多以前没有出现过，突出了与经典理论的差异和相似之处。
Kolmogorov-Sinai entropy is an invariant of measure-preserving actions of the group of integers that is central to classification theory. There are two recently developed invariants, sofic entropy and Rokhlin entropy, that generalize classical entropy to actions of countable groups. These new theories have counterintuitive properties such as factor maps that increase entropy. This survey article focusses on examples, many of which have not appeared before, that highlight the differences and similarities with classical theory.