Almost reducibility of linear difference systems from a spectral point of view

Abstract

We prove that, under some conditions, a linear nonautonomous difference system is Bylov's almost reducible to a diagonal one whose terms are contained in the Sacker and Sell spectrum of the original system. We also provide an example of the concept of diagonally significant system, recently introduced by P\"otzche. This example plays an essential role in the demonstration of our results.