走向现代数学学术报告 - 王晓东副教授（No. 553）

报告题目：Multifractal analysis of singular hyperbolic attractors

报 告 人：王晓东 副教授（上海交通大学）

报告时间：2022年11月15日 16:30

线上报告：腾讯会议730-404-437

摘要：We study the multifractal analysis for singular hyperbolic attractors, including the geometric Lorenz attractors. For each singular hyperbolic homoclinic class whose periodic orbits are all homoclinically related and such that the space of ergodic probability measures is connected, we prove that: (i) level sets associated to continuous observables are dense in the homoclinic class and satisfy a variational principle; (ii) irregular sets are either empty or are Baire generic and carry full topological entropy. The assumptions are satisfied by C¹-generic singular hyperbolic attractors and C^r-generic geometric Lorenz attractors (r≥2). The main technique we apply is the horseshoe approximation property. This is a joint work with Y. Shi, X. Tian and P. Varandas.

报告人简介：王晓东，上海交通大学副教授，2016年博士毕业于北京大学&巴黎萨克雷大学，研究方向为微分动力系统和遍历论，在Ergodic Theory and Dynamical Systems, Nonlinearity, Israel Journal of Mathematics等杂志发表多篇论文。