TY - JOUR
T1 - Almost reduction and perturbation of matrix cocycles
AU - Bochi, Jairo
AU - Navas, Andrés
N1 - Publisher Copyright:
© 2013 Elsevier Masson SAS. All rights reserved.
PY - 2014/11/1
Y1 - 2014/11/1
N2 - 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.
AB - 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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U2 - 10.1016/j.anihpc.2013.08.004
DO - 10.1016/j.anihpc.2013.08.004
M3 - Article
AN - SCOPUS:84912150049
SN - 0294-1449
VL - 31
SP - 1101
EP - 1107
JO - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
JF - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
IS - 6
ER -