学术报告报告主题: 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17日（星期五）下午16:00-17:00
报告地点：37号楼3A02
邀 请 人: 李兵 教授
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数学学院
2026年4月14日
报告摘要：
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 $X(a,b)$.
专家简介：
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. He is the main organiser of the (online) One World Numeration Seminar.