走向现代数学学术报告 - 马东魁教授（No. 789)

报告题目：TOPOLOGICAL ENTROPY, TOPOLOGICAL PRESSURE OF FREE SEMIGROUP ACTIONS FOR NON-COMPACT SETS AND SOME APPLICATIONS

报 告 人：马东魁 教授（华南理工大学）

邀 请 人：李健 教授

报告时间：2025年5月11日（星期日）10:30

报告地点：东海岸校区-D实232

报告摘要：In this talk, we adopt the Caratheodory-Pesin structure(C-P structure) and introduce the notions of the topological entropy(pressure) and lower and upper capacity topological entropies(pressure) of a free semigroup action for an arbitrary subset. We provide some properties of these notions. As applications, we give some estimations of the topological entropy(pressure) or upper capacity topological entropy of a free semigroup action on certain non-compact sets. By using the Bowen’s equation with respect to the topological pressure, we characterize the Hausdorff dimension of an arbitrary subset, where the points of the subset have the positive lower Lyapunov exponents and satisfy a tempered contraction condition. Our analysis generalizes the results obtained by Bufetov, Misiurewicz, Ma-Wen, Huang, Tian, Chen, Lau and Climenhaga et al..

报告人简介：马东魁，华南理工大学数学学院教授，博士生导师，主要研究领域为拓扑动力系统、遍历论及其应用，在包括ETDS，JDE，DCDS，JSP等刊物上发表论文50余篇，主持及参与国家自然科学基金和广东省基金多项。