论文标题
统一晶格以外的小组动作的熵
Entropy of group actions beyond uniform lattices
论文作者
论文摘要
可符合离散组的量度保存或连续作用的熵允许采用各种等效方法。其中是Ollagnier和Pinchon一方面开发的技术，另一方面是Ornstein-Weiss引理。我们将这两种方法扩展到了正式拓扑群体的行动背景。与离散设置相反，我们的结果揭示了非污染群体领域的两个熵概念之间存在显着差异：而在非差异情况下，第一个数量崩溃到0，而第二个数量则产生了良好的不可测量群体的行为良好的不变性。关于后者，我们还研究了拓扑压力的相应概念，证明是goodwyn型定理，并使用均匀的晶格方法（对于局部紧凑的群体承认均匀的晶格）建立了等效性。我们的研究详细介绍了由于Gromov引起的Ornstein-Weiss引理的版本。
Entropy of measure preserving or continuous actions of amenable discrete groups allows for various equivalent approaches. Among them are the ones given by the techniques developed by Ollagnier and Pinchon on the one hand and the Ornstein-Weiss lemma on the other. We extend these two approaches to the context of actions of amenable topological groups. In contrast to the discrete setting, our results reveal a remarkable difference between the two concepts of entropy in the realm of non-discrete groups: while the first quantity collapses to 0 in the non-discrete case, the second yields a well-behaved invariant for amenable unimodular groups. Concerning the latter, we moreover study the corresponding notion of topological pressure, prove a Goodwyn-type theorem, and establish the equivalence with the uniform lattice approach (for locally compact groups admitting a uniform lattice). Our study elaborates on a version of the Ornstein-Weiss lemma due to Gromov.
