The Brjuno functions and their regularity properties

Communications in Mathematical Physics

Volumn 186, Issue 2, 1997, Pages 265-293

  Marmi, S ^a   Moussa, P ^b   Yoccoz, J C ^c  

^a UNIVERSITY OF FLORENCE   (Italy)

^b CEA SACLAY   (France)

^c UNIVERSITÉ PARIS SACLAY   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031548111     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200050110     Document Type: Article

References (20)

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3. Brjuno, A. D.: Analytical form of differential equations. Trans. Moscow Math. Soc. 25, 131-288 (1971); 26, 199-239 (1972)
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5. Davie, A. M.: The critical function for the semistandard map. Nonlinearity 7, 219-229, (1994). The same author has announced similar results for the standard map (private communication)
6. ème Série 18, 287-343 (1985)
7. 1, Leipzig: Teubner, 1917, p. 372
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12. Marmi, S., Moussa, P., Yoccoz, J.-C.: Continued fraction transformations, Brjuno functions, and BMO spaces. Note CEA-N-2788, Feb. 1995. This internal report is in fact a preliminary version of the present work
13. Marmi, S. Stark, J.: On the standard map critical function. Nonlinearity 5, 743-761 (1992)
14. Meyer, D. H.: On a ζ-function related to the continued fraction transformation. Bull. Soc. Math. France 104, 195-203 (1976)
15. Meyer, D. H.: On the Thermodynamic Formalism for the Gauss Map. Commun. Math. Phys. 130, 311-333 (1990)
16. Meyer, D. H.: Continued fractions and related transformations. In: Ergodic theory, symbolic dynamics and hyperbolic spaces, T. Bedford, M. Keane, C. Series, editors, Oxford: Oxford University Press, 1991
17. Nakada, H.: On the invariant measures and the entropies for continued fraction transformations. Keio Math. Rep. 5, 37-44 (1980)
18. Pérez-Marco, R.: Solution complète au problème de Siegel de linéarisation d'une application holomorphe au voisinage d'un point fixe. Séminaire Bourbaki nr. 753, Astérisque 206, 273-310 (1992)
19. Rieger, G. J.: Mischung und Ergodizität bei Kettenbruchen nach nächsten genzen. J. Reine Angew. Math. 310, 171-181 (1979)
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