Hostname: page-component-848d4c4894-ttngx Total loading time: 0 Render date: 2024-06-04T04:29:03.814Z Has data issue: false hasContentIssue false
  • English
  • Français

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)
Get access Rights & Permissions [Opens in a new window]

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) .

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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