报告题目：Bohr chaoticity of topological dynamical systems

报告人：范爱华 教授

报告时间：2024年12月19日9：00-

报告地点：数统4号楼312

邀请单位：福州大学数学与统计学院(肖祖彪)

报告内容简介：We introduce the Bohr chaoticity, which is a complexity of a dynamical system and is a topological invariant. The Bohr chaoticity of a system implies the positivity of the system's 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 discussd.

报告人简介：范爱华教授为法国Picardie大学特级教授。师从法国科学院院士Kahane教授，曾先后入选国家杰青（B类）等多项国家级人才计划。其研究领域涉及几何测度论、调和分析、概率论与随机过程、动力系统与遍历理论，p-进分析与p-进算术动力系统; 发表学术论文120余篇。