Communications in Mathematical Physics

, Volume 186, Issue 2, pp 265–293 | Cite as

The Brjuno Functions and Their Regularity Properties

  • S. Marmi
  • P. Moussa
  • J.-C. Yoccoz


We show that various possible versions of the Brjuno function, based on different kinds of continued fraction developments, are all equivalent and we study their regularity (L p, BMO and Hölder) properties, through a systematic analysis of the functional equation which they fulfill.


Functional Equation Continue Fraction Regularity Property Fraction Development Brjuno Function 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • S. Marmi
    • 1
  • P. Moussa
    • 2
  • J.-C. Yoccoz
    • 3
  1. 1.Dipartimento di Matematica “U. Dini”, Università di Firenze, 50134 Firenze, Italy IT
  2. 2.CEA, Service de Physique Théorique, CE-Saclay, F-91191 Gif-sur-Yvette Cedex, FranceFR
  3. 3.Université de Paris-Sud, Mathématiques, Bât. 425, 91405 Orsay, FranceFR

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