Abstract
The arithmetics of the frequency and of the rotation number play afundamental role in the study of reducibility of analyticquasiperiodic cocycles which are sufficiently close to a constant.In this paper we show how to generalize previous works byL.H. Eliasson which deal with the diophantine case so as to implementa Brjuno-Rüssmann arithmetical condition both on the frequency and onthe rotation number. Our approach adapts the Pöschel-Rüssmann KAMmethod, which was previously used in the problem of linearization ofvector fields, to the problem of reducing cocycles.
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