no. 6
Almost reduction and perturbation of matrix cocycles
Annales de l'I.H.P. Analyse non linéaire, Tome 31 (2014) no. 6, pp. 1101-1107.

In this note, we show that if all Lyapunov exponents of a matrix cocycle vanish, then it can be perturbed to become cohomologous to a cocycle taking values in the orthogonal group. This extends a result of Avila, Bochi and Damanik to general base dynamics and arbitrary dimension. We actually prove a fibered version of this result, and apply it to study the existence of dominated splittings into conformal subbundles for general matrix cocycles.

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     title = {Almost reduction and perturbation of matrix cocycles},
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Bochi, Jairo; Navas, Andrés. Almost reduction and perturbation of matrix cocycles. Annales de l'I.H.P. Analyse non linéaire, Tome 31 (2014) no. 6, pp. 1101-1107. doi : 10.1016/j.anihpc.2013.08.004. http://www.numdam.org/articles/10.1016/j.anihpc.2013.08.004/

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