微分动力系统学术报告

报告题目: On the multifractal analysis for singular hyperbolic attractors

报告人：王晓东（上海交通大学）

时间： 2022-09-21 09:30-10:30

腾讯会议：387-118-158

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 C^1-generic singular hyperbolic attractors and C^r-generic geometric Lorenz attractors (r≥2).  The main technique we apply is the horseshoe approximation property.

邀请人：文晓、张金华