Measure Complexity and Rigid Systems

• 作者: Wen HUANG Run Ju WEI Tao YU Xiao Min ZHOU
• 来源期刊: 数学学报（英文版）
• 年，卷（期）: 2022,（1）
• 页码范围: 68-84
• 页数: 17页
• 语种: 英文

摘要

In this paper we introduce two metrics:the max metricdn,qand the mean metric-dn,q.We give an equivalent characterization of rigid measure preserving systems by the two metrics.It turns out that an invariant measure μ on a topological dynamical system(X,T)has bounded complexity with respect to dn,q if and only if μ has bounded complexity with respect to-dn,q if and only if(X,Bx,μ,T)is rigid.We also obtain computation formulas of the measure-theoretic entropy of an ergodic measure preserving system(resp.the topological entropy of a topological dynamical system)by the two metrics dn,q and-dn,q.