Reducibility of quasiperiodic cocycles under a Brjuno-Rüssmann arithmetical condition

Claire Chavaudret; Stefano Marmi

doi:10.3934/jmd.2012.6.59

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2012, Volume 6, Issue 1: 59-78. Doi: 10.3934/jmd.2012.6.59

This issue Previous Article On primes and period growth for Hamiltonian diffeomorphisms Next Article Hölder foliations, revisited

Reducibility of quasiperiodic cocycles under a Brjuno-Rüssmann arithmetical condition

Claire Chavaudret^1, and
Stefano Marmi^2,

1.
Département deMathématiques, Université de Nice Sophia-Antipolis, Parc Valrose, 06108 Nice Cedex 02
2.
Scuola Normale Superiore, Piazza dei Cavalieri, 7, 56126, Pisa (PI)

Received: October 31, 2011

Published: April 2012

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Abstract

The arithmetics of the frequency and of the rotation number play a fundamental role in the study of reducibility of analytic quasiperiodic 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-Rüssmann arithmetical condition both on the frequency and on the rotation number. Our approach adapts the Pöschel-Rüssmann KAM method, which was previously used in the problem of linearization of vector fields, to the problem of reducing cocycles.

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Mathematics Subject Classification: Primary: 34C20; Secondary: 37CXX.

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References

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