双符号等长代换系统的序列熵

张国华;匡锐;叶向东

数学学报 ›› 2005, Vol. 48 ›› Issue (5) : 833-840.

PDF(528 KB)
PDF(528 KB)
数学学报 ›› 2005, Vol. 48 ›› Issue (5) : 833-840. DOI: 10.12386/A2005sxxb0101
论文

双符号等长代换系统的序列熵

    张国华;匡锐;叶向东
作者信息 +

Topological Sequence Entropy of Substitutions of Constant Length on Two Symbols

    Guo Hua ZHANG, Rui KUANG, Xian
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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.

Abstract

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 arc 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

拓扑序列熵 / 极小系统 / 子代换

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张国华;匡锐;叶向东. 双符号等长代换系统的序列熵. 数学学报, 2005, 48(5): 833-840 https://doi.org/10.12386/A2005sxxb0101
Guo Hua ZHANG, Rui KUANG, Xian. Topological Sequence Entropy of Substitutions of Constant Length on Two Symbols. Acta Mathematica Sinica, Chinese Series, 2005, 48(5): 833-840 https://doi.org/10.12386/A2005sxxb0101
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