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arXiv · 1301.5464

Almost reduction and perturbation of matrix cocycles

Jairo Bochi·Andrés Navas
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Abstract

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 of general matrix cocycles.

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Jairo Bochi, Andrés Navas. 2013-01-23. Almost reduction and perturbation of matrix cocycles. https://doi.org/10.1016/j.anihpc.2013.08.004

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