Reducibility of cocycles under a Brjuno-Rüssmann arithmetical condition

Claire Chavaudret (1) , Stefano Marmi (2)

1 JAD - Laboratoire Jean Alexandre Dieudonné
2 SNS PISA - Gruppo di ricerca di sistemi dinamici

The arithmetics of the frequency and of the rotation number play a fundamental role in the study of reducibility of analytic quasi-periodic cocycles which are sufficiently close to a constant. In this paper we show how to generalize previous works by L.H.Eliasson which deal with the diophantine case so as to implement a Brjuno-Russmann arithmetical condition both on the frequency and on the rotation number. Our approach adapts the Poschel-Russmann KAM method, which was previously used in the problem of linearization of vector fields, to the problem of reducing cocycles.

Mots clés: cocycle; quasiperiodic; reducibility; Brjuno; Rüssmann; rotation number

Domaines: Systèmes dynamiques [math.DS]

Claire Chavaudret, Stefano Marmi. Reducibility of cocycles under a Brjuno-Rüssmann arithmetical condition. Journal of modern dynamics, 2012, 6 (1), pp.59-78. ⟨hal-00610394v2⟩