We describe the average behaviour of the Brjuno function Φ in the neighbourhood of any given point of the unit interval. In particular, we show that the Lebesgue set of Φ is the set of Brjuno numbers and we find the asymptotic behaviour of the modulus of continuity of the integral of Φ.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm218-3-1,
author = {Michel Balazard and Bruno Martin},
title = {Comportement local moyen de la fonction de Brjuno},
journal = {Fundamenta Mathematicae},
volume = {219},
year = {2012},
pages = {193-224},
zbl = {1287.26006},
language = {fra},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm218-3-1}
}
Michel Balazard; Bruno Martin. Comportement local moyen de la fonction de Brjuno. Fundamenta Mathematicae, Tome 219 (2012) pp. 193-224. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm218-3-1/