走向现代数学学术报告 - 侯晓博博士（No. 695）

报告题目：Abundance of Smale's horseshoes and ergodic measures via multifractal analysis and various quantitative spectrums

报 告 人：侯晓博 博士（复旦大学）

报告时间：2024年4月19日（星期五）10:30

地点：东海岸校区-D实209

摘要：In this talk we consider intermediate entropy property under the observation of continuous functions. On one hand this refined the Katok's intermediate entropy property to get a multifractal version. On the other hand it helps us to get the intermediate properties of Hausdorff dimension geometric pressure, unstable Hausdorff dimension, first return rate, Lyapunov exponents etc. The considered systems include uniformly hyperbolic diff. or flows, nonuniformly hyperbolic diff. or singular hyperbolic flows, and many symbolic dynamics. In this process, we introduce and establish a ‘multi-horseshoe’ entropy-dense property and use it to get the goal combined with the well known conditional variational principles.

报告人简介：侯晓博，2023年6月博士毕业于复旦大学，现在复旦大学数学科学学院从事博士后研究工作。主要研究方向是微分动力系统和遍历理论，在Ergodic Theory and Dynamical Systems，Nonlinearity，Discrete and Continuous Dynamical Systems等学术期刊发表论文多篇，获得中国博士后科学基金74批面上资助。