报告人:王保伟 (华中科技大学)

时  间:2018年12月21日  15:00--16:00

地  点:理科楼 LD202

摘  要:Dynamical Diophantine approximation concerns the Diophantine properties of the orbit in a dynamical system. More precisely, let $(X,T)$ be a dynamical system with a metric $|\cdot|$. One concerns the size of the following limsup set defined via a dynamical system: $$W(\psi):=\Big\{x\in X: |T^nx-y|<\psi(n,x), \ {\text{i.o.}}, n\in \N\Big\}.$$ Following Hill \& Velani's pioneer work [Invent. Math. 95'], there have been many works done in concrete dynamical systems. We hope to find a general principle about the dimension of $W(\psi)$ in a general framework. By introducing a {\em dynamical ubiquity property}, it is shown that in an expanding exact topological dynamical system, when $\psi(n,x)=e^{-(f(x)+\cdots+f(T^{n-1}x))}$, both the dimension of $X$ and $W(\psi)$ are given by the solution to some pressure functions. While from the dimension of $X$ to that of $W(\psi)$, one needs only transfer the potential in the pressure equation. For this partial analogy with the mass transference principle in classic Diophantine approximation [Beresvenich \& Velani, Ann. of Math. 06'], we call the above phenomenon  as a {\em dynamical dimension transference principle.} This is a joint with Guahua Zhang.

报告人简介:王保伟，男，华中科技大学教授。研究方向是分形几何与度量丢番图逼近。先后主持国家自然科学基金青年基金、面上项目和优秀青年基金，入选教育部“新世纪优秀人才支持计划”。在Adv. Math.、Proc. Lond. Math. Soc.、Ergodic Theory & Dynam. Systems 等知名数学杂志上发表三十多篇学术论文。

学院联系人:罗 军

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