no. 4
Estimates of the linearization of circle diffeomorphisms
[Estimées de la linéarisation de difféomorphismes du cercle]
Bulletin de la Société Mathématique de France, Tome 142 (2014) no. 4, pp. 673-718

A celebrated theorem by Herman and Yoccoz asserts that if the rotation number α of a C∞-diffeomorphism of the circle f satisfies a Diophantine condition, then f is C∞-conjugated to a rotation. In this paper, we establish explicit relationships between the Ck norms of this conjugacy and the Diophantine condition on α. To obtain these estimates, we follow a suitably modified version of Yoccoz's proof.

Un célèbre théorème de Herman et Yoccoz affirme que si le nombre de rotation α d'un C∞-difféomorphisme du cercle f satisfait une condition diophantienne, alors f est C∞-conjugué à une rotation. Dans cet article, nous établissons des relations explicites entre les Ck normes de cette conjuguée et la condition diophantienne sur α. Pour obtenir ces estimées, nous suivons une version convenablement modifiée de la preuve de Yoccoz.

Publié le :
DOI : 10.24033/bsmf.2676
Classification : 37C05
Keywords: Circle diffeomorphisms, rotation number, conjugacy, estimates.
Mots-clés : Difféomorphismes du cercle, nombre de rotation, conjuguée, estimées. 
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Benhenda, Mostapha. Estimates of the linearization of circle diffeomorphisms. Bulletin de la Société Mathématique de France, Tome 142 (2014) no. 4, pp. 673-718. doi: 10.24033/bsmf.2676

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