91自拍 学术报告[2026]032号

(高水平大学建设系列报告1291号)

报告题目：Ordered binary shifts with a hole

报告人：Wolfgang Steiner  教授（法国巴黎西岱大学）

报告时间：2026年4月19日11:00-12:00

报告地点：汇文楼2433

报告内容：Let $X(a,b)$ be the set of binary sequences such that no shifted sequence lies in the interval (of sequences) [a,b]. When the interval is taken with respect to the lexicographic order, this can also be seen as the survivor set of the doubling map with a hole or of a beta-transformation with a hole at 0, or as the set of trajectories of a Lorenz map, and it is now well known for which pairs (a,b) the shift space $X(a,b)$ is non-trivial or has positive topological entropy. We consider two other orders on sequences: the alternating lexicographic order and the unimodal order, which correspond to the negative doubling map and the tent map. Glendinning (1993, 2014) has studied maps of this type, and recently Glendinning and Hege characterised positive topological entropy via renormalizations. We revisit their results on the symbolic level, describe precisely the occurring renormalizations, and give formulae for the entropy of $X(a,b)$ and for the Hausdorff dimension of the set of double base expansions given by $X(a,b)$.

报告人简历：Wolfgang Steiner is Austrian and has obtained his PhD with Michael Drmota in Vienna. Since 2005, he has a CNRS research position at the Institut de Recherche en Informatique Fondamentale (IRIF) in Paris. He is mainly interested in various aspects of numeration systems (dynamical, combinatorial, number theoretical, geometrical, ...), in particular of beta-expansions and continued fractions.

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邀请人：邹玉茹

91自拍

2026年4月18日