报告人: Karma Dajani （荷兰乌特勒支大学）

日  期: 2019年11月28日

时  间: 15:00

地  点: 理科楼 LA106

摘 要: We consider the concept of Minkowski normality, a different type of normality for the regular continued fraction expansion. We use the ordering

1/2； 1/3，2/3；1/4，3/4，2/5，3/5；…

of rationals obtained from the Kepler tree to give a concrete construction of an infinite continued fraction whose digits are distributed according to the Minkowski question mark measure. This is done by defining an explicit correspondence between continued fraction expansions and binary codes to show that we can use the dyadic Champernowne number to prove normality of the constructed number. Furthermore, we provide a generalized construction based on the underlying structure of the Kepler tree, which shows that any construction that concatenates the continued fraction expansions of all rationals, ordered so that the sum of the digits of the continued fraction expansion are non-decreasing, results in a number that is Minkowski normal. As a consequence we can construct normal numbers based on the Calkin-Wilf tree, as well as normal numbers for the Farey map and certain families of GLS-expansions. This is joint work with M. de Lepper and E.A. Robinson

报告人简介：Karma Dajani 教授，现工作于荷兰乌特勒支大学数学系，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。 Dajani教授是欧洲数学界具有很高知名度的女性数学家，在J. Eur. Math. Soc.，Trans. Amer. Math. Soc.等数学杂志上发表论文50多篇，她和Cornelis Kraaikamp教授合作的专著《Ergodic Theory of Numbers》已成该领域的一本非常重要的参考书，是很多高校数学系分形几何方向的研究生教材。

学院联系人:孔德荣

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