Almost reduction and perturbation of matrix cocycles
Dynamical Systems
2015-06-12 v2
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.
Keywords
Cite
@article{arxiv.1301.5464,
title = {Almost reduction and perturbation of matrix cocycles},
author = {Jairo Bochi and Andrés Navas},
journal= {arXiv preprint arXiv:1301.5464},
year = {2015}
}
Comments
10 pages, no figures. A few corrections were made in this version