完备度量空间中的混沌判定

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完备度量空间中的混沌判定吴小英, 陈员龙, 王芬广东金融学院金融数学与统计学院广州 510521 Chaotic Criteria in Complete Metric Spaces Xiao Ying WU, Yuan Long, CHEN Fen WANGSchool of Financial Mathematics and Statistics, Guangdong University of Finance, Guangzhou 510521, P. R. China

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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Λ，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.

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收稿日期: 2019-02-26

MR (2010):

O19

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

通讯作者:陈员龙,E-mail:chernylong@163.comE-mail: chernylong@163.com

引用本文:

吴小英, 陈员龙, 王芬. 完备度量空间中的混沌判定[J]. 数学学报, 2021, 64(2): 225-230. Xiao Ying WU, Yuan Long, CHEN Fen WANG. Chaotic Criteria in Complete Metric Spaces. Acta Mathematica Sinica, Chinese Series, 2021, 64(2): 225-230.

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