论文标题
熵，产品和有限的轨道等效性
Entropy, products, and bounded orbit equivalence
论文作者
论文摘要
我们证明，如果在紧凑的可迁移空间上可计数的sofic群体的两个无拓扑和熵的定期操作是连续的轨道等效物，并且每个组都包含一个W范式的可符合的亚组，则既不是局部有限的，也不是实际上循环的，或（ii）是非局限性的组成组的，然后是两个无限限制的概述，然后是两种动作，而是属于两种行动。然后使用此事实表明，如果此类组的两个自由独特的巨像和熵的常规概率可衡量的动作是有界轨道等效的，那么这些动作具有相同的SOFIC度量熵。我们的论点是基于财产SC与SOFIC近似的相对性，并产生更多的一般熵不平等。
We prove that if two topologically free and entropy regular actions of countable sofic groups on compact metrizable spaces are continuously orbit equivalent, and each group either (i) contains a w-normal amenable subgroup which is neither locally finite nor virtually cyclic, or (ii) is a non-locally-finite product of two infinite groups, then the actions have the same sofic topological entropy. This fact is then used to show that if two free uniquely ergodic and entropy regular probability-measure-preserving actions of such groups are boundedly orbit equivalent then the actions have the same sofic measure entropy. Our arguments are based on a relativization of property SC to sofic approximations and yield more general entropy inequalities.
