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

Published online by Cambridge University Press:  01 November 2008

DOYONG KWON
DOYONG KWON*
Affiliation:
Pohang Mathematics Institute, Department of Mathematics, POSTECH, Pohang 790-784, Republic of Korea. e-mail: doyong@postech.ac.kr
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Abstract

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

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 145 , Issue 3 , November 2008 , pp. 739 - 756
Copyright
Copyright © Cambridge Philosophical Society 2008

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