报告时间：2023年4月12日（周三） 10:00–11:00

报告地点：理学院五楼数学研究中心报告厅

报告题目：Lyapounov exponent of deterministic product of non-negative matrices and Multifractal analysis of weighted Birkhoff averages

报告摘要：The Lyapounov exponent of random product of non-negative matrices exists almost surely by Furstenberg-Kesten theorem or Kingman theorem. But both Furstenberg-Kesten theorem and Kingman theorem tell us nothing about a given sample of matrices. We find conditions to ensure the existence of Lyapounov exponent for EVERY generic choice of matrices. If one of matrices from which we select our matrices is of rank one, we find a closed formula for the Lyapounov exponent. Application is given to the multifractal analysis of weighted Birkhoff averages.

报告人简介：范爱华，教授，博士生导师，法国Picardie大学教授，现受聘华中师范大学教授。2001年入选教育部“长江学者”特聘教授及中国科学院百人计划；2008年获国家基金委的海外合作基金(B类杰青)。曾任法国国家科研中心LAMFA实验室概率论和遍历理论研究室主任以及国家基金委面上基金和重点基金特邀评委；教育部学科评估评审专家；教育部科技成果奖评审专家。主要研究领域是动力系统和遍历理论、概率论、Fourier分析和分形几何等。