关于IFS的一个经典遍历定理的注记  

A Note on a Classical Ergodic Theorem for IFS

作　　者：杨荣领 马东魁 YANG Rongling;MA Dongkui(School of Computer Engineering,Guangzhou City University of Technology,Guangzhou 510800,China;School of Mathematics,South China University of Technology,Guangzhou 510640,China)

机构地区：[1]广州城市理工学院计算机工程学院,广州510800 [2]华南理工大学数学学院,广州510640

出　　处：《华南师范大学学报（自然科学版）》2022年第4期109-112,共4页Journal of South China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11771149)。

摘　　要：给出了Elton定理不成立的点构成的集合的性质:通过构造符号空间中的柱集,证明了对一个具有概率的压缩IFS,连续函数g满足∫_(X) g dν_(1)≠∫_(X) g dν_(2),ν_(1)和ν_(2)表示IFS中2个不同的不变测度,则Elton定理不成立的点构成的零测集要么是空集,要么是具有满Hausdorff维数和满拓扑熵的集合。The properties of the set of points where Elton’s theorem does not hold are given. By constructing cylinder sets in symbolic space, it is proved that for a contractive IFS with probabilities and a continuous function g sa-tisfying that ∫gdν≠∫gdν, where νand νare any two different invariant measures of the IFS, the zero measure invariant set composed of points where Elton’s theorem does not hold is either empty or carries full Hausdorff dimension and topological entropy.

关 键 词：IFS Elton定理 拓扑熵 HAUSDORFF维数 

分 类 号：O189[理学—数学]