动力系统的复杂性刻划

本文扼要地综述了近年来提出的刻划动力系统复杂性的各种度量．着重点在于将复杂性同随机性区分开．由此对于过去为刻划混沌而提出的度量，其中包括Ｌｙａｐｕｎｏｖ指数、拓扑熵、测度熵和Ｋｏｌｍｏｇｏｒｏｖ复杂性等，作了简单回顾．从自动机和信息论的观点对于包括ＡＣ、ＳＣ、ＥＭＣ在内的新提出的复杂性度量作了阐述．通过单峰映射和一维元胞自动机等例子对上述复杂性度量进行了比较，并较详细地介绍了利用形式语言和自动机来分析动力系统的方法． 

CHARACTERIZING COMPLEXITY OF DYNAMICAL SYSTEMS

This paper gives an overview of different measures of complexity proposed to characterize dynamical systems developed during recent years. The emphasis is placed on the distinction of complexity from randomness. Those measures, which were used to characterize chaos, including Lyapunov exponent,topologic al entropy, metric entropy, Kolmogorov complexity etc., are reviewed briefly in this sense. New measures, including AC, SC, EMC among others,are explained from the point of view of both automata and information theory.Through the examples o f unimodal maps and one-dimensional cellular automata,the above-mentioned measures of complexity are compared, and the method of using formal languages and automata to analyze dynamical systems is elucidated in detail.