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The Brjuno Functions and Their Regularity Properties

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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.

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Authors and Affiliations

  1. Dipartimento di Matematica “U. Dini”, Università di Firenze, 50134 Firenze, Italy , , , , , , IT

    S. Marmi

  2. CEA, Service de Physique Théorique, CE-Saclay, F-91191 Gif-sur-Yvette Cedex, France, , , , , , FR

    P. Moussa

  3. Université de Paris-Sud, Mathématiques, Bât. 425, 91405 Orsay, France, , , , , , FR

    J.-C. Yoccoz

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  1. S. Marmi
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  2. P. Moussa
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  3. J.-C. Yoccoz
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Received: 21 March 1995 / Accepted: 8 August 1996

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Marmi, S., Moussa, P. & Yoccoz, JC. The Brjuno Functions and Their Regularity Properties . Comm Math Phys 186, 265–293 (1997). https://doi.org/10.1007/s002200050110

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  • DOI: https://doi.org/10.1007/s002200050110

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