A condition of Boshernitzan and uniform convergence in the multiplicative ergodic theorem

Abstract

This article is concerned with uniform convergence in the multiplicative ergodic theorem on aperiodic subshifts. If such a subshift satisfies a certain condition, originally introduced by Boshernitzan [6], [7], every locally constant SL(2,R)-valued cocycle is uniform. As a consequence, the corresponding Schrodinger operators exhibit Cantor spectrum of Lebesgue measure zero