一维动力系统的语法复杂性  

GRAMMATICAL COMPLEXITY OF ONE-DIMENSIONAL DYNAMICAL SYSTEMS

作　　者：陈曦[1] 卢钦和[1] 谢惠民[1] 

机构地区：[1]苏州大学数学系

出　　处：《苏州大学学报（自然科学版）》1993年第1期68-72,共5页Journal of Soochow University(Natural Science Edition)

基　　金：国家基础性研究重大项目<非线性科学>的资助

摘　　要：本文证明了由单峰映射确定的形式语言为正规语言的充分必要条件是该映射的揉序列为周期或终极周期序列.将这个结果与Jacobson定理比较,可见存在不可列个单峰映射,它们的复杂程度高于正规语言.In this paper we prove that for formal languages,which are determined by-kneading sequences of unimodal mappings,being regular languages,it is necessary and sufficient that their kneading sequences are either periodic or eventually periodic. Combining this result with Jacobson Theorem, we see that there are uncountably many systems which have higher degrees of complexity than those of regular languages.

关 键 词：单峰映射 复杂性 动力系统 语法 

分 类 号：O411[理学—理论物理]