迭代函数系统的强跟踪性质  

The Strong Shadowing g Property for Iterated Function Systems

作　　者：曾鹏 陈昌华 李远飞 ZENG Peng;CHEN Chang-hua;LI Yuan-fei(School of Data Science,Guangzhou Huashang College,Guangzhou 511300,China;Guangzhou Railway Polytechnic,Guangzhou 510430,China)

机构地区：[1]广州华商学院数据科学学院,广东广州511300 [2]广州铁路职业技术学院基础学部,广东广州510430

出　　处：《数学的实践与认识》2023年第1期207-214,共8页Mathematics in Practice and Theory

基　　金：广州华商学院校内导师制项目(2022HSDS09);广东省青年创新人才项目(2020KQNCX132);广州市哲学社会科学发展“十三五”规划课题(2019GZGJ209)。

摘　　要：给出了迭代函数系统(IFS(F))的强跟踪性质的概念并且研究了它的相关性质.结合经典动力系统的相关方法,首先证明了一致压缩的迭代函数系统都有强跟踪性质,从而给出了具有强跟踪性质的相关例子;另外也证明了两个IFS(F)的强跟踪性质在拓扑共轭的条件下是保持不变的;最后我们得到了:如果IFS(F)有小距离扩张性,则它是开的当且仅当它具有强跟踪性质.In this paper,we introduce the notion of the strong shadowing property for iterated function systems(IFS(F))and prove some related theorems on this notion.First,we prove that every uniformly contracting IFS(F)has the strong shadowing property,and give some examples with the strong shadowing property;in addition,we also prove that the strong shadowing property of two IFS(F)is invariant under the condition of topological conjugation;finally,we prove that if IFS(F)expands small distance,then it is open if and only if it has the strong shadowing property.

关 键 词：迭代函数 强跟踪性质 一致压缩 拓扑共轭 

分 类 号：O19[理学—数学]