Comportement local moyen de la fonction de Brjuno

TL;DR

This paper investigates the average behavior of the Brjuno function near any point in the unit interval, identifying its Lebesgue set as the Brjuno numbers and analyzing the asymptotic behavior of its integral's modulus of continuity.

Contribution

It characterizes the Lebesgue set of the Brjuno function and determines the asymptotic behavior of its integral's modulus of continuity.

Findings

The Lebesgue set of the Brjuno function coincides with the set of Brjuno numbers.

The paper establishes the asymptotic behavior of the modulus of continuity of the integral of the Brjuno function.

Abstract

We describe the average behaviour of the Brjuno function in the neighbourhood of any given point of the unit interval. In particular, we show that its Lebesgue set is the set of Brjuno numbers and we fi nd the asymptotic behaviour of the modulus of continuity of its integral.