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 $\mathrm{SL}(2,\mathbb{R})$-valued cocycle is uniform. As a consequence, the corresponding Schrödinger operators exhibit Cantor spectrum of Lebesgue measure zero