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

• Autores: Doyong Kwon
• Localización: Mathematical proceedings of the Cambridge Philosophical Society, ISSN 0305-0041, Vol. 145, Nº 3, 2008, págs. 739-756
• Idioma: inglés
• DOI: 10.1017/s0305004108001606
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• Resumen

  • 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.