复合系统的混沌性  

Chaos in the Compositional Systems

作　　者：吴新星[1] 朱培勇[1] 

机构地区：[1]电子科技大学数学科学学院,成都四川611731

出　　处：《数学进展》2013年第3期405-415,共11页Advances in Mathematics（China）

基　　金：国家自然科学基金(No.10671134);四川省教育厅科研基金(No.12ZA098)

摘　　要：本文讨论复合系统混沌性与原系统混沌性之间的联系.首先证明:在紧度量空间上,所有的复合系统都保持原系统的Li-Yorke混沌性,并且用反例说明,在一般的度量空间,该结论不成立.其次,研究复合系统的分布混沌性,得到和Li-Yorke混沌相似的结论.最后,用实例说明:对于任意的正整数n≥2,存在紧致Devaney混沌系统,其n次复合系统却不是Devaney混沌的.This paper is devoted to studying the relations between the chaoticity of compositional systems and primary systems. First, it is proved that on a compact metric space, all the compositional systems preserve Li-Yorke＇s chaoticity of the primary systems. And a counterexample is given to show that on a general metric space, this conclusion does not hold. Next, we study the distributional chaoticity of compositional systems and obtain some conclusions which are similar to Li-Yorke chaos. Finally, we use an example to show that for any n ≧ 2, there exists a compact system which is chaotic in the sense of Devaney, but its nth compositional system is not.

关 键 词：Li—Yorke混沌 分布混沌 DEVANEY混沌 初值敏感依赖 

分 类 号：O189.11[理学—数学]