A devil's staircase from rotations and irrationality measures for Liouville numbers

Details A devil's staircase from rotations and irrationality measures for Liouville numbers A devil's staircase from rotations and irrationality measures for Liouville numbers

2007-09-11

arxiv.org/abs/0709.1642v1

Mathematics

Number Theory

This version was updated. The older one is available at http://math.yonsei.ac.kr/doyong

Scientific paper

10.1017/S0305004108001606

From Sturmian and Christoffel words we derive a strictly increasing function $\Delta:[0,\infty)\to\mathbb{R}$. This function is continuous at every irrational point, while at rational points, left-continuous but not right-continuous. Moreover, it assumes algebraic integers at rationals, and transcendental numbers at irrationals. We also see that the differentiation of $\Delta$ distinguishes some irrationality measures of real numbers.

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