报告题目：On the existence and coexistence of expansivity

报告人：梁兵兵 教授（苏州大学数学科学学院）

报告时间：2022年9月22日14：00-15：00

报告地点：腾讯视频会议（线上）

会议ID：224-636-185   会议密码：220922

校内联系人：江永乐 副教授  联系电话：84708351-8033

报告摘要：Expansivity is an important property in dynamical systems. Given a discrete group G and a compact metric space X, it is a basic question to ask whether G can act on X expansively. A classical result due to Kato shows that the integer group can NOT expansively act on Suslinian continua (including the unit interval). We extend this result to the action by finitely generated group of subexponential growth. The proof is built upon a delicate characterization of expansivity due to Meyerovitch-Tsukamoto and Kato’s characterization of Suslinian continua.

In regard to the coexistence of expansivity with other dynamical properties, we show that if a continuous action of a finitely generated group on a compact metric space is both distal and expansive, then the phase space must be finite. A counterexample is constructed to show that the condition of finite generation is indispensable. Moreover, if the phase space is connected and the acting group is any countable group, Hanfeng Li proves that the phase space must be a singleton.

These results are joint works with Enhui Shi, Zhiwen Xie, and Hui Xu.

报告人简介：梁兵兵，苏州大学数学科学学院特聘教授，美国纽约州立大学布法罗分校获博士学位，曾在德国波恩马普所从事博士后研究，以及波兰科学院数学研究所担任助理教授职位。研究领域为算子代数和拓扑动力系统交叉方向。论文发表在综合且历史悠久的[J. Reine Angew. Math.]、[Adv.Math.]杂志以及[Ergodic Theory Dynam. Systems]、 [J. Funct. Anal.]等国际权威数学期刊。