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 for general matrix cocycles.

Original languageEnglish (US)
Pages (from-to)1101-1107
Number of pages7
JournalAnnales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume31
Issue number6
DOIs
StatePublished - Nov 1 2014

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematical Physics
  • Applied Mathematics

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