非自治动力系统中序列跟踪性和渐进平均跟踪性的研究  

The Research of Sequence ShadowingProperty and Asymptotic Average Shadowing Property in NonautonomousDynamical Systems

作　　者：冀占江 JI Zhan-jiang(Applied Mathematics Research Team of the Research Academy of Science,Wuzhou University,Wuzhou 543002,China;Guangxi Key Laboratory of Machine Vision and Intelligent Control,Wuzhou University,Wuzhou 543002,China)

机构地区：[1]梧州学院科学研究院应用数学研究团队,广西梧州543002 [2]梧州学院广西机器视觉与智能控制重点实验室,广西梧州543002

出　　处：《数学的实践与认识》2024年第6期231-235,共5页Mathematics in Practice and Theory

基　　金：广西自然科学基金(2020JJA110021,2023JJB160018)。

摘　　要：在非自治动力系中引入序列跟踪性、渐进平均跟踪性和强链回归点的概念,然后在非自治动力系统中研究序列跟踪性和渐进平均跟踪性的动力学性质以及强链回归点集的拓扑结构,若序列映射F={f_(k)}^(∞)_(k=0)拓扑共轭于序列映射G={g_(k)}^(∞)_(k=0),则有如下结果:1)F具有序列跟踪性当且仅当G具有序列跟踪性;2)F具有渐进平均踪性当且仅当G具有渐进平均踪性;3)h(SCR(F)=SCR(G).It is introduced that the concept of sequence shadowing property,asymptotic average shadowing property and strong chain recurrent point in the nonautonomous dynamical system.Then,we study the dynamic properties of sequence tracking and asymptotic average tracking and the topological structure of strong chain recurrent point sets in nonautonomous dynamical systems.If the sequence maps F={f_(k)}^(∞)_(k=0) is topologically conjugate to sequence maps G={g_(k)}^(∞)_(k=0),then the following results can be obtained.1)F has sequence shadowing property if and only if G has sequence shadowing property;2)F has asymptotic average shadowing property if and only if G has asymptotic average shadowing property;3)h(SCR(F))=SCR(G).

关 键 词：非自治动力系统 渐进平均跟踪性 强链回归点集 

分 类 号：O19[理学—数学]