理学院“格物论坛学术报告”（三十一）

理学院“格物论坛学术报告”（三十一）

报 告 人： 马东魁 教授

报告题目：Topological entropy of free semigroup actions for noncompact sets and its applications

报告时间：2021年5月29日（周六） 10:00-11:00
报告地点：理生楼A502

报告人简介：

马东魁，男，华南理工大学数学学院教授，博士生导师，美国《数学评论》的评论员，主要研究方向为拓扑动力系统与遍历论,  主持、参与国家自然科学面上基金5项， 在Ergodic Theory Dynam. Systems、 Discrete & Continuous Dynamical Systems-等数学期刊上发表学术论文40余篇。

报告摘要：

We introduce the topological entropy and lower and upper capacity topological entropy of a free semigroup action, which extend the notion of the topological entropy of a free semigroup action defined by Bufetov, by using the Carath ́eodory-Pesin structure (C-P structure). We provide some properties of these notions and give three main results. The first is the relationship between the upper capacity topological entropy of a skew- product transformation and the upper capacity topological entropy of a free semigroup action with respect to arbitrary subset. The second are a lower and an upper estimations of the topological entropy of a free semigroup action by local entropy. The third is that for any free semigroup action with m generators of Lipschitz maps, topological entropy for any subset is upper bounded by the Hausdorff dimension of the subset multiplied by the maximum logarithm of the Lipschitz constants. The results of this talk generalize the results of Bufetov , Ma et al., and Misiurewicz. Finally, we give some applications.

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主办单位：南昌大学科技处, 南昌大学理学院数学系