报告人：廖灵敏 教授（武汉大学）

时间：2026年01月08日 10:30-

地点：理科楼LA104

摘要：Given $\alpha \in [0,1]$, we study the set of numbers sharing identical representation of regular continued fractions and $\alpha$-continued fractions. It turns out that such set have the same Hausdorff dimension as that of a survivor set of the Gauss map with a hole at $1$, i.e., the set of points $x$ such that all the iterations under Gauss map of $x$ is less than $\alpha$. We show that the function of the Hausdorff dimensions of such sets associated to $\alpha$ is increasing and locally constant almost everywhere. Further, we show that it is not continuous at $0$, which is a new phenomenon in the study of open dynamical systems. This is a joint work with Cheng LIU.

邀请人：数学研究中心

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