Bohr chaoticity and Related questions

：范爱华（法国Picardie大学）
：2024-05-07 16:00
：海韵园数理大楼686会议室

报告人：范爱华（法国Picardie大学）

时  间：2024年5月7日16:00

地  点：海韵园数理大楼686会议室

内容摘要:

The Bohr chaoticity is a complexity of a dynamical system and is a topological invariant; it implies the positivity of entropy. However, the positivity of entropy doesn’t imply the Bohr chaoticity. We prove that a system (X, T) admitting a horseshoe (i.e a susbsytem of some power of T is conjugate to a full shift) is Bohr chaotic. Thus the usual nice systems of positive entropy are Bohr chaotic. But systems having few ergodic measures are not Bohr chaotic.  Another class of systems which are proved to be Bohr chaotic are the algebraic principal systems.  These are joint works with Shilei FAN (Wuhan), Valery RYZHYKOV (Moscou), Klaus SCHMIDT (Vienna), Weixiao SHEN (Shanghai) and Evgeny VERBITSKIY (Leiden). Some related questions will be discussed.

个人简介：

范爱华，法国Picardie大学特级教授，武汉大学特聘教授，Wallenberg访问教授 (瑞典隆德大学)。博士毕业于法国南巴黎大学。主要研究方向：动力系统与遍历理论，傅立叶分析，几何测度论，概率论与随机混沌等。系列成果发表在Proc LMS, Math Ann, Adv Math, Tran AMS, CMP, JFA等学术期刊。多次获得国家级高层次人才计划支持。

 

联系人：朱玉峻