Almost reduction and perturbation of matrix cocycles
Annales de l'I.H.P. Analyse non linéaire, Volume 31 (2014) no. 6, p. 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.

@article{AIHPC_2014__31_6_1101_0,
     author = {Bochi, Jairo and Navas, Andr\'es},
     title = {Almost reduction and perturbation of matrix cocycles},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Elsevier},
     volume = {31},
     number = {6},
     year = {2014},
     pages = {1101-1107},
     doi = {10.1016/j.anihpc.2013.08.004},
     zbl = {1332.37026},
     mrnumber = {3280061},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2014__31_6_1101_0}
}
Bochi, Jairo; Navas, Andrés. Almost reduction and perturbation of matrix cocycles. Annales de l'I.H.P. Analyse non linéaire, Volume 31 (2014) no. 6, pp. 1101-1107. doi : 10.1016/j.anihpc.2013.08.004. http://www.numdam.org/item/AIHPC_2014__31_6_1101_0/

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