The Hilbert cube contains a minimal subshift of full mean dimension

：乔艺晓（广东工业大学）
：2024-03-15 10:30
：海韵园实验楼110报告厅

报告人：乔艺晓（广东工业大学）

时  间：2024年3月15日10:30

地  点：海韵园实验楼110报告厅

内容摘要:

In this talk I shall address an embedding problem in relation to mean dimension theory, which concerns the connection between embedding possibility and mean dimension at a critical value for minimal dynamical systems. I will present its historical background briefly, and give a complete solution to this problem. More precisely, we prove that the shift action on the Hilbert cube contains a minimal subshift of full mean dimension. In contrast to dimension theory and entropy theory, this is a different phenomenon in mean dimension theory. The proof is constructive. Our result, in company with all the previously known results in this direction, leads eventually to a full understanding of the embedding possibility of minimal dynamical systems in Hilbert cubes with a view towards mean dimension. This is a joint work with Lei Jin. 

个人简介：

乔艺晓，广东工业大学数学与统计学院副教授；2018年获得中国科学技术大学和波兰科学院数学研究所（IMPAN）基础数学博士学位。研究方向是拓扑动力系统，尤其是平均维数（mean dimension）理论以及与其相关的动力学嵌入问题；研究论文发表于GAFA, Math. Ann., Sci. China Math., JDE, Nonlinearity, ETDS, Studia Math.等学术期刊；主持国家自然科学基金青年项目和面上项目。

 

联系人：朱玉峻