Comportement local moyen de la fonction de Brjuno
Volume 218 / 2012
Fundamenta Mathematicae 218 (2012), 193-224
MSC: Primary 26A27; Secondary 11A55.
DOI: 10.4064/fm218-3-1
Abstract
We describe the average behaviour of the Brjuno function $\varPhi $ in the neighbourhood of any given point of the unit interval. In particular, we show that the Lebesgue set of $\varPhi $ is the set of Brjuno numbers and we find the asymptotic behaviour of the modulus of continuity of the integral of $\varPhi $.
