1.Adrianova, L. Ja., The reducibility of systems of n linear differential equations with quasi-periodic coefficients, Vestnik Leningrad. Univ. 17(7) (1962), 14–24.
2.Avila, A., Fayad, B. and Krikorian, R., A KAM scheme for SL(2, ℝ) cocycles with Liouvillean frequencies, Geom. Funct. Anal. 21(5) (2011), 1001–1019.
3.Avila, A. and Krikorian, R., Reducibility or non-uniform hyperbolicity for quasiperiodic Schrödinger cocycles, Ann. of Math. (2) 164(3) (2006), 911–940.
4.Arnold, V. I., Chapitres supplémentaires de la théorie des équations différentielles ordinaires. Mir, 1980.
5.Chavaudret, C., Strong almost reducibility for analytic and Gevrey quasi-periodic cocycles, Bull. Soc. Math. France 141(1) (2013), 47–106.
6.Chavaudret, C. and Marmi, S., Reducibility of quasiperiodic cocycles under a Brjuno-Rüssmann arithmetical condition, J. Mod. Dyn. 6(1) (2012), 59–78.
7.Eliasson, L. H., Floquet solutions for the 1-dimensional quasi-periodic Schrödinger equation, Comm. Math. Phys. 146(3) (1992), 447–482.
8.Eliasson, L. H., Almost reducibility of linear quasi-periodic systems, in Smooth Ergodic Theory and its Applications (Seattle, WA, 1999), Proceedings of Symposia in Pure Mathematics, Volume 69, pp. 679–705 (American Mathematical Society, Providence, RI, 2001).
9.He, H.-L. 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.
10.Johnson, R. and Moser, J., The rotation number for almost periodic potentials, Comm. Math. Phys. 84(3) (1982), 403–438.
11.Krikorian, R., Réductibilité des systèmes produits-croisés à valeurs dans des groupes compacts, Astérisque (259) 1999.
12.Krikorian, R., Réductibilité presque partout des flots fibrés quasi-périodiques à valeurs dans des groupes compacts, Ann. Sci. Éc. Norm. Supér. (4) 32(2) (1999), 187–240.
13.Mitropol’skiĭ, Ju. A. and Samoĭlenko, A. M., On constructing solutions of linear differential equations with quasiperiodic coefficients by the method of improved convergence, Ukraïn Mat. Zh. 17(6) (1965), 42–59.
14.Stolovitch, L., Forme normale de champs de vecteurs commutants, C. R. Acad. Sci. I 324 (1997), 665–668.
15.Zhou, Q. and Wang, J., Reducibility results for quasiperiodic cocycles with Liouvillean frequency, J. Dynam. Differential Equations 24(1) (2012), 61–83.
${\it\omega}$
, namely, a vector whose coordinates are not linearly independent over 
$\mathbb{Z}$
. We give sufficient conditions that ensure that a small analytic perturbation of a constant system is analytically conjugate to a ‘resonant cocycle’. We also apply our results to the non-resonant case: we obtain sufficient conditions for reducibility.
