Shape of Metric Entropy
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：蒋云平
：2021-07-08 10:00
：腾讯会议 ID：566715784（无密码）
报告人：蒋云平（美国纽约城市大学）
时 间：7月8日上午10:00
地 点：腾讯会议 ID：566715784（无密码）
内容摘要: In this talk, I will mention a joint work with Huyi Hu and Miaohua Jiang on constructing smooth paths in the same type of Anosov or area preserving Anosov dynamical systems, which are in the space of Anosov and area preserving Blaschke products respectively. The metric entropy takes any value from zero+ to the topological entropy. The former tends to an almost Anosov Blaschke product which is smoothly conjugate to the famous Boole map, giving a new explanation of Boole's formula, and the latter tends to a totally degenerate map. These two paths represent the same smooth path in the space of all smooth conjugacy classes of Anosov Blaschke products, which enables me to prove a global graph of the metric entropy on such space and obtain a complete description of the shape of the metric entropy. Furthermore, I provide a global picture of the measure-theoretic entropy on the main cardioid of the Mandelbrot set for the Gibbs measures.
个人简介：
蒋云平，美国纽约城市大学杰出教授（Distinguished Professor）。1982年毕业于北京大学数学系，1990年毕业于美国纽约城市大学，获博士学位。蒋云平教授是中科院百人计划入选者，并多次在美国获得国家和学校的科学研究奖励。蒋云平教授曾任美国数学学会的著名杂志Memoirs of the AMS 和Transactions of the AMS编委。蒋云平教授的研究方向是动力系统，研究兴趣主要集中在一维动力系统，复动力系统，在Comm. Math. Phys., Adv. Math., Trans. AMS, Ergodic Theory Dynam. Systems, Chaos等权威学术期刊发表论文80多篇。
联系人：朱玉峻
