完备度量空间中的混沌判定  

Chaotic Criteria in Complete Metric Spaces

作　　者：吴小英 陈员龙 王芬 Xiao Ying WU;Yuan Long CHEN;Fen WANG(School of Financial Mathermatics and Statistics,Guangdong University of Finance,Guangzhou 510521,P.R.China)

机构地区：[1]广东金融学院金融数学与统计学院,广州510521

出　　处：《数学学报（中文版）》2021年第2期225-230,共6页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金(11671410,61907010);广东省自然科学基金(2017A030313037,2018A0303130120);广东省普通高校自然科学重点项目(2019KZDXM036)。

摘　　要：本文研究完备度量空间上的离散动力系统的混沌标准,证明了如果完备度量空间X上的连续映射f具有正则非退化返回排斥子或连接不动点的正则非退化异宿环,则存在f的不变闭子集A,使得f限制在此不变闭子集上的子系统与两个符号的符号动力系统拓扑共轭,从而获得具有这类结构的连续映射f具有Devaney混沌、分布混沌、正拓扑熵及ω-混沌,此结果改进了已有的相关结果.In this paper,the chaotic criteria of discrete dynamical systems is studied in complete metric spaces.It is showed that if f is continuous map from a complete metric space X into itself and has regular nondegenrate snap-back repellers or heteroclinic repellers,then there exists an invariant subset A of f such that(A,f)is topologically conjugate to the one-side symbolic system(∑2^(+),σ).Therefore,f is Devaney’s chaos,distributional chaos,ω-chaos and has positive entropy.These results improve the related results.

关 键 词：离散动力系统 DEVANEY混沌 分布混沌 返回排斥子 拓扑共轭 

分 类 号：O19[理学—数学]