A+ CATEGORY SCIENTIFIC UNIT

Comportement local moyen de la fonction de Brjuno

Volume 218 / 2012

Michel Balazard, Bruno Martin 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 $.

Authors

  • Michel BalazardInstitut de Mathématiques de Luminy
    UMR 6206
    CNRS, Aix Marseille Université
    Campus de Luminy, Case 907
    13288 Marseille Cedex 9, France
    e-mail
  • Bruno MartinLaboratoire de Mathématiques Pures
    et Appliquées
    CNRS, Université du Littoral Côte d'Opale
    50 rue F. Buisson, BP 599
    62228 Calais Cedex, France
    e-mail

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