动力系统中F-传递性与F-混合性的一个注记  

A remark of F-transitive and F-mixed properties in dynamical systems

作　　者：姜文雅 张思汇[1] 刘杰[2] JIANG Wenya;ZHANG Sihui;LIU Jie(College of Science,University of Shanghai for Science and Technology,Shanghai 200093,China;School of Mathematics and Statistics,Nanjing University of Science and Technology,Nanjing 210094,China)

机构地区：[1]上海理工大学理学院,上海200093 [2]南京理工大学数学与统计学院,南京210094

出　　处：《上海理工大学学报》2024年第4期427-430,共4页Journal of University of Shanghai For Science and Technology

基　　金：国家自然科学基金资助项目(11971233)。

摘　　要：对一维动力系统的混合性及传递性进行了一般性讨论。设(I,f)是一个拓扑动力系统(简称动力系统或系统),其中I为紧致度量空间(度量为d),f:X→X是连续映射。基于Furstenberg族,研究了一维动力系统(I,f)和它的泛函包络系统(L^(1)(I,I),H_(f))的一些性质,在前人研究的混合性和传递性的基础上,引进了F–混合与F–传递的概念,并证明了如果(I,f)是F–混合的,则(L^(1)(I,I),H_(f))是F–传递的。The mixed and transitive properties of one-dimensional dynamic systems were generally discussed.Here,the(I,f) was defined as a topological dynamical system(referred to as a dynamical system or system),where I was a compact metric space(metric wasd) and f:X→X was a continuous map.Based on the Furstenberg family,several properties of the one-dimensional dynamical system(I,f)and its functional envelope system(L^(1)(I,I),H_(f)) were studied.Based on the mixed and transitive properties studied by previous people,the concept of F-mixed and F-transitive were introduced.The results can help prove that if(I,f) is F-mixed,and then(L^(1)(I,I),H_(f)) is F-transitive.

关 键 词：F–传递 F–混合 泛函包络 

分 类 号：O19[理学—数学]