具有零拓扑熵的图映射的攀援集的测度  

On the Measure of Scrambled Sets of Graph Maps with Zero Topological Entropy

作　　者：匡锐 梁先娟 KUANG Rui;LIANG Xianjuan(School of Mathematics,South China University of Technology,Guangzhou,Guangdong,510641,P.R.China;Department of Mathematics,Shantou University,Shantou,Guangdong,515063,P.R.China)

机构地区：[1]华南理工大学数学学院,广州广东510641 [2]汕头大学数学系,汕头广东515063

出　　处：《数学进展》2021年第2期315-319,共5页Advances in Mathematics（China）

基　　金：Supported by NSFC (Nos.11401220,11671094,11771264);NSF of Guangdong Province(Nos.2018B0303110005,2018B030306024)。

摘　　要：本文研究了具有零拓扑熵的图映射f的性质,证明了在任意有限f-不变的Borel测度μ下,其攀援集的外μ-测度都是零.In this paper,it is shown that any scrambled set of a graph map f with zero topological entropy has zero outer μ-measure,where μ is any finite and f-invariant Borel measure.

关 键 词：图映射 混沌 攀援集 拓扑熵 不变测度 

分 类 号：O192[理学—数学]