Comportement local moyen de la fonction de Brjuno

Michel Balazard (1) , Bruno Martin (2)

1 IML - Institut de mathématiques de Luminy
2 LMPA - Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville

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.

Mots clés: Brjuno function; Brjuno numbers; Lebesgue set; Continued fractions.

Mots clés: Continued fractions

Domaines: Théorie des nombres [math.NT]; Systèmes dynamiques [math.DS]

Michel Balazard, Bruno Martin. Comportement local moyen de la fonction de Brjuno. Fundamenta Mathematicae, 2012, 218 (3), p. 193-224. ⟨10.4064/fm218-3-1⟩. ⟨hal-00723616⟩