题目：Multi-horseshoe dense property and intermediate entropy property of ergodic measures with same level
时间：2023年4月20日10:00-11:00
地点：数学院425
报告人：侯晓博博士，复旦大学数学科学学院
邀请人：肖映青
摘要: We combine the perspectives of entropy, topology, and multifractal analysis to investigate ergodic measures. On one hand, we prove that for a transitive locally maximal hyperbolic set or a transitive two-sided subshift of finite type $(X,f)$, any continuous function $\varphi$ on $X$ and for any $(a,h)\in \mathrm{Int}\{(\int \varphi d\mu, h_\mu(f)):\mu\in \mathcal{M}_f(X)\},$ the set $\{\mu\in \mathcal{M}_f^e(X): (\int \varphi d\mu, h_\mu(f))=(a,h)\}$ is non-empty and contains a dense $G_\delta$ subset of $\{\mu\in \mathcal{M}_f(X): (\int \varphi d\mu, h_\mu(f))=(a,h)\}.$ On the other hand, we generalize this result to multiple functions and use it to obtain the intermediate Hausdorff dimension of ergodic measures. In this process, we introduce and establish a 'multi-horseshoe' entropy-dense property and use it to get the goal combined with conditional variational principles. This is a joint work with Yiwei Dong and Xueting Tian.
