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}, pages = {1101--1107}, publisher = {Elsevier}, volume = {31}, number = {6}, year = {2014}, doi = {10.1016/j.anihpc.2013.08.004}, mrnumber = {3280061}, zbl = {1332.37026}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2013.08.004/} }
TY - JOUR AU - Bochi, Jairo AU - Navas, Andrés TI - Almost reduction and perturbation of matrix cocycles JO - Annales de l'I.H.P. Analyse non linéaire PY - 2014 SP - 1101 EP - 1107 VL - 31 IS - 6 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2013.08.004/ DO - 10.1016/j.anihpc.2013.08.004 LA - en ID - AIHPC_2014__31_6_1101_0 ER -
%0 Journal Article %A Bochi, Jairo %A Navas, Andrés %T Almost reduction and perturbation of matrix cocycles %J Annales de l'I.H.P. Analyse non linéaire %D 2014 %P 1101-1107 %V 31 %N 6 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2013.08.004/ %R 10.1016/j.anihpc.2013.08.004 %G en %F 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/articles/10.1016/j.anihpc.2013.08.004/
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