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Comportement local moyen de la fonction de Brjuno

Michel BalazardBruno Martin — 2012

Fundamenta Mathematicae

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.

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