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

Doyong Kwon

• From Sturmian and Christoffel words we derive a strictly increasing function ?:[0,8) ? . 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 ? distinguishes some irrationality measures of real numbers.