文献类型：期刊文献

英文题名：A NOTE ON TOPOLOGICALLY TRANSITIVE TREE MAPS

作者：Li, Risong[1,4];Lu, Tianxiu[2];Quan, Weizhen[3];Pi, Jingmin[2]

机构：[1]Guangdong Ocean Univ, Sch Math & Comp Sci, Zhanjiang 524025, Peoples R China;[2]Sichuan Univ Sci & Engn, Coll Math & Stat, Zigong 643000, Peoples R China;[3]Zhanjiang Presch Educ Coll, Dept Math, Zhanjiang 524037, Peoples R China;[4]Bridge Nondestruct Detecting & Engn Comp Key Lab, Artificial Intelligence Key Lab Sichuan Prov, Zigong 643000, Peoples R China

年份：2020

卷号：12

期号：5

起止页码：1801

外文期刊名：JOURNAL OF APPLIED ANALYSIS AND COMPUTATION

收录：SCI-EXPANDED(收录号：WOS:000878405600001)、、WOS

基金：This work was supported by the Project of Department of Science and Technology of Sichuan Provincial (No. 2021ZYD0005), the Opening Project of Artificial Intelligence Key Laboratory, and Bridge Non-destruction Detecting and Engineering Computing Key Laboratory (Nos. 2018RZJ03, 2018QZJ03), Ministry of Education Science and Technology Development Center (No. 2020QT13) and Characteristic innovation project of colleges and universities in Guangdong Province in 2020 (No. 2020KTSCX351).

语种：英文

外文关键词：Sensitivity; topologically mixing; topologically weak mixing; topological transitive; cofinitely sensitive

外文摘要：In this note, W is a tree. F : W -> W is a continuous map. k(W) = {C subset of W : C not equal empty set and C is compact} is endowed with a Hausdorff metric. The paper gives a sufficient and necessary condition under which F is topologically transitive. Furthermore, it is shown that both a topologically transitive tree map F :W -> W and the continuous map (F ) over bar on k(W) which is induced by F are cofinitely sensitive, where (F) over bar (C) = {F(x) : x is an element of C} for any C is an element of k(W).