Almost reduction and perturbation of matrix cocycles

Jairo Bochi; Andrés Navas

doi:10.1016/j.anihpc.2013.08.004

Almost reduction and perturbation of matrix cocycles

Jairo Bochi
, Andrés Navas

Mathematics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

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 for general matrix cocycles.

Original language	English (US)
Pages (from-to)	1101-1107
Number of pages	7
Journal	Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume	31
Issue number	6
DOIs	https://doi.org/10.1016/j.anihpc.2013.08.004
State	Published - Nov 1 2014

All Science Journal Classification (ASJC) codes

Analysis
Mathematical Physics
Applied Mathematics

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10.1016/j.anihpc.2013.08.004

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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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Almost reduction and perturbation of matrix cocycles

Abstract

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