Journal of Modern Dynamics (JMD)

Reducibility of quasiperiodic cocycles under a Brjuno-Rüssmann arithmetical condition

Pages: 59 - 78, Issue 1, January 2012      doi:10.3934/jmd.2012.6.59

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Claire Chavaudret - Département deMathématiques, Université de Nice Sophia-Antipolis, Parc Valrose, 06108 Nice Cedex 02, France (email)
Stefano Marmi - Scuola Normale Superiore, Piazza dei Cavalieri, 7, 56126, Pisa (PI), Italy (email)

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.

Keywords:  Quasiperiodic cocycle, Brjuno condition, diophantine condition, rotation number, reducibility, KAM method.
Mathematics Subject Classification:  Primary: 34C20; Secondary: 37CXX.

Received: November 2011;      Available Online: May 2012.