报告人: Cornelis Kraaikamp （荷兰代尔夫特理工大学）

日  期: 2019年11月28日

时  间: 16:00

地  点: 理科楼 LA106

摘 要: In 1991 a new class of continued fraction expansions, the $S$-expansions, was introduced. This class contains many classical continued fraction algorithms, such as Nakada’s $\alpha$-expansions (for $\alpha$ between 1/2 and 1), the nearest integer continued fraction, Minkowski’s diagonal continued fraction expansion, and Bosma’s optimal continued fraction. These $S$-expansions were obtained from the natural extension of the regular continued fraction (RFC) via induced transformations. Therefore many metric and arithmetic properties of these $S$-expansions can be derived from the corresponding classical results on the RFC. In particular, the natural extensions of these $S$-expansions were obtained. The second coordinate map of these natural extensions is the inverse of a continued fraction algorithm. In a recent paper my co-author Irene Ravesloot and I study these ‘reversed algorithms’; in particular we show they are again $S$-expansions, and we find the corresponding singularization areas. In this talk I will outline our work, which appeared in Acta Arithmetica 190 (2019), 363-380.

报告人简介：Cornelis Kraaikamp教授，现工作于荷兰代尔夫特理工大学数学系，主要从事beta展式、连分数、动力系统遍历论等方面的研究工作。到目前为止，Kraaikamp教授在J. Eur. Math. Soc.，Trans. Amer. Math. Soc.等数学杂志上发表论文60多篇。他与Karma Dajani教授合作的专著《Ergodic Theory of Numbers》已成为该领域研究的一本非常重要的参考书，被很多大学作为研究生教材。

公司联系人:孔德荣

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