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Reducibility of quasiperiodic cocycles in linear Lie groups

Published online by Cambridge University Press:  10 May 2010

CLAIRE CHAVAUDRET
CLAIRE CHAVAUDRET*
Affiliation:
Institut de Mathématiques de Jussieu, 175 rue du Chevaleret, 75013 Paris, France (email: chavaudret@math.jussieu.fr)
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Abstract

Let G be a linear Lie group. We define the G-reducibility of a continuous or discrete cocycle modulo N. We show that a G-valued continuous or discrete cocycle which is GL(n,ℂ)-reducible is in fact G-reducible modulo two if G=GL(n,ℝ),SL(n,ℝ),Sp(n,ℝ) or O(n) and modulo one if G=U(n) .

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 31 , Issue 3 , June 2011 , pp. 741 - 769
Copyright
Copyright © Cambridge University Press 2010

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References

[1]Cassels, J. W. S.. An Introduction to the Geometry of Numbers. Springer, Berlin, 1997.Google Scholar
[2]Eliasson, L. H.. Almost reducibility of linear quasi-periodic systems (Proceedings of Symposia in Pure Mathematics, 69), 2001, pp. 697–705.Google Scholar
[3]He, H. and You, J.. Full-measure reducibility for generic one-parameter family of quasi-periodic linear systems. J. Dynam. Differential Equations 20(4) (2008), 831–866.Google Scholar
[4]Krikorian, R.. Réductibilité des systémes produit croisé à valeurs dans des groupes compacts. Astérisque 259 (1999).Google Scholar
[5]Krikorian, R.. Réductibilité presque partout des flots fibré quasi-périodiques à valeurs dans des groupes compacts. Ann. Sci. École Norm. Sup. (4) 32(2) (1999), 187–240.CrossRefGoogle Scholar