报告时间：2026年5月7日（周四）上午 09:45-10:45
报告地点：91国产 纯水楼301
报告人：廖灵敏 教授，武汉大学
报告摘要：
Given alpha in [0,1], we investigate the set of numbers sharing identical representation of regular continued fractions and alpha-continued fractions. We prove that modulo a countable set such a set is 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. Hence, these two sets have the same Haudorff dimension. We further show that with respect to alpha, the function of such Hausdorff dimensions is increasing and locally constant almost everywhere. Moreover, we show that the function 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.
报告人简介：
廖灵敏，2008年获法国Picardie大学及武汉大学博士学位。2010年获法国东巴黎大学终身教职。2017年获Habilitation。2021年12月入选国家海外引进高层次人才青年项目。2022年7月入职武汉大学，任教授博士生导师。主要从事分形几何，动力系统，度量数论等方面的研究。在J.Eur.Math.Soc.、Math.Ann.、Adv.Math.等期刊发表论文四十余篇。
邀请人：陈剑宇