Multidimensional Multiplicative Large Sets in Totally Minimal Systems  

作　　者：Jian Jie ZHAO 

机构地区：[1]School of Mathematics,Hangzhou Normal University,Hangzhou 311121,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2023年第8期1635-1649,共15页数学学报（英文版）

基　　金：supported by the Scientific Research Fund of Zhejiang Provincial Education Department(Grant No.Y202147669);the Zhejiang Provincial Natural Science Foundation of China(Grant No.LQ23A010006)。

摘　　要：In this paper,it is shown that for a residual set of points in a totally minimal system with finitely many commuting homeomorphisms,the set of return times to any non-empty open set contains a subset with positive multidimensional multiplicative upper Banach density,extending a previous result by Glasscock,Koutsogiannis and Richter.Meanwhile,we give some combinatorial properties of the sets with positive multidimensional multiplicative upper Banach density.

关 键 词：Multidimensional multiplicative upper Banach density totally minimal systems 

分 类 号：O19[理学—数学]