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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

Abstract:

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.

Keywords

Functional Equation Continue Fraction Regularity Property Fraction Development Brjuno Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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