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Pré-Publication, Document De Travail Année : 2011

Estimates of the Linearization of Circle Diffeomorphisms

Résumé

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

hal-00628297 , version 1 (02-10-2011)

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  • HAL Id : hal-00628297 , version 1

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Mostapha Benhenda. Estimates of the Linearization of Circle Diffeomorphisms. 2011. ⟨hal-00628297⟩
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