双符号等长代换系统的序列熵  

Topological Sequence Entropy of Substitutions of Constant Length on Two Symbols

作　　者：张国华[1] 匡锐[1] 叶向东[1] 

机构地区：[1]中国科学技术大学数学系,合肥230026

出　　处：《数学学报（中文版）》2005年第5期833-840,共8页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金973资助项目

摘　　要：系统称为null的,如果对任意序列,它的序列熵为零.双符号等长代换及其对应的代换极小系统可分成三类:有限的、离散的和连续的.容易看出离散的代换极小系统是null的,Goodman证明了连续的代换极小系统不是null的.本文将完全刻画所有的双符号等长代换极小系统的序列墒.A dynamical system is null if its sequence entropy is zero for any sequence. Substitutions of constant length on two symbols and their corresponding minimal dynamical systems are divided into three types： finite, discrete and continuous. It is easy to see that such a substitution of finite type is null, and Goodman showed that the one of continuous type is not null. In this paper we completely determine which substitution of discrete type is null.

关 键 词：极小系统 子代换 拓扑序列墒 

分 类 号：O189.1[理学—数学] O192[理学—基础数学]