ON GRAMMATICAL COMPLEXITY OF A CLASS OF ATTRACTORS

ＯＮＧＲＡＭＭＡＴＩＣＡＬＣＯＭＰＬＥＸＩＴＹＯＦＡＣＬＡＳＳＯＦＡＴＴＲＡＣＴＯＲＳＬｕＱｉｎｈｅ（卢钦和）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ．ＳｕｚｈｏｕＵｎｉｖｅｒｓｉｔ｝＇．Ｓｕｚｈｏｕ２１５００６．Ｐ．Ｒ．Ｃｈｉｎａ）Ａｂｓｔ...     

Grammatical Complexity of Feigenbaum Attractor

The Feigenbaum attractor is an important case in the dynamical systems of one-dimensional maps . In this paper we analyze the grammatical complexity of theFeigenbaum attractor, using both theories of symbolic dynamics and of formal lan-guages . In the Chomsky's hierarchy, formal languages are classified into fourlevels: regular languages, context-free languages, context-sensitive languages and re-cursively enumerable languages. It was shown in [6] that for one-dimensional cellularautomata, the sets of configurations generated after a finite number of time steps of     

广义Feigenbaum吸引子的语法复杂性

本文研究了由周期ｎ分岔（Ｐｅｒｉｏｄ－ｎ－ｔｕｐｌｉｎｇ）生成的广义Ｆｅｌｇｅｎｂａｕｍ吸引子的揉序列，讨论了由揉序列决定的形式语言Ｌ的语法复杂性，证明了它是上下文有关语言（ＣＳＬ）而不是上下文无关语言（ＣＦＬ）。     

The global bifurcation structure of a kind of digit mapping

The global structure of the mapping T_n:x→[x~2]_n,is studied.The symmetricunconnected substructures of T_2 is coincident with[1]by computer,but for n=3 thesymmetry of these substructures vanishes.As n is increasing,the global bifurcationstructure of T_n is shown.Finally,similar results for the mapping T_n,μ:x→[μx~2 ]_n are alsoproved.     

Lozi映射奇怪吸引子的探讨

本文利用横截环理论,详细分析了Lozi映射的奇怪吸引子的存在性和结果,所得结果与数值结果相吻合,并解释了若干数值现象,从而进一步论证[1]所提出奇怪吸引子结论是合理的。     

一类数字映射的全局结构

本文讨论映射T_n:x→[x~2]_n的全局结构.T_2具有对称的不连通子结构的性质和[1]用计算机得到的结果一致.但当n=3时,这些子结构不再具有对称性了.本文得到随n增大时T_n的全局分叉结构,并得到了映射T_n,μ:x→[μx~2]_n的类似结果.     

一类吸引子的语法复杂性*

本文研究了Feigenbaum吸引子和周期窗口中Feisenbaum吸引子决定的形式语言,讨论了它们的语法复杂性.证明了这类吸引子都是ETOL语言,从而是上下文有关语言(CSL);而不是上下文无关语言(CFL).