Ergodicity of partially hyperbolic systems

讲座题目：Ergodicity of partially hyperbolic systems

讲座时间 Datetime: 2025年12月08日，周一，15:00-16:00

地点 Venue:海琴二号 A457

主持人 Host：Sergio Augusto Romana Ibarra副教授.

报告人 Speaker: Ziqiang Feng 博士后研究员

单位 Affiliation:北京大学

报告摘要 Abstract:

Ergodicity, originally introduced by Boltzmann in 19th century as a hypothesis in thermodynamics, has been extensively studied as a powerful framework for formulating the equidistribution of typical orbits in dynamical systems. Using the argument introduced by Hopf, the so-called "Hopf argument", and developed by Anosov and Sinai, it is well-known that all $C^2$ volume-preserving uniformly hyperbolic systems are ergodic. However, the adaptation of Hopf argument to the partially hyperbolic context becomes significantly complicated due to the presence of non-hyperbolic distribution. The famous Stable Ergodicity Conjecture proposed by Pugh-Shub 30-years ago asserts the prevalence of ergodicity among volume-preserving partially hyperbolic systems. I will present our results jointly with Raul Ures on characterizing this prevalence, giving advances to the Hertz-Hertz-Ures Ergodicity Conjecture.

报告人简介：

Ziqiang Feng is currently a postdoc at Beijing International Center for Mathematical Research (BICMR), Peking University. Previously, he received his doctor degree from SUSTech, under supervision of Prof. Raul Ures, and served as a visiting research scholar at Penn State University.