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 mul...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.展开更多
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)。
文摘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.
