标题： 一维准晶的勒贝格测度零奇异谱 显示英文标题

标题： Singular spectrum of Lebesgue measure zero for one-dimensional quasicrystals

摘要： 与严格遍历动力系统的关联的一维离散薛定谔算符的谱当且仅当李雅普诺夫指数处处存在时才与李雅普诺夫指数的零点集重合。 这被用来得到所有具有一致正权值的非周期次移位的零勒贝格测度的康托尔谱。 这尤其涵盖了由本原替代产生的所有非周期次移位，包括新的例子，如Rudin-Shapiro替代。 我们的研究不是基于迹线映射。 相反，它依赖于A. Furman的一个Oseledec型定理和作者的一个一致遍历定理。 显示英文摘要

摘要： The spectrum of one-dimensional discrete Schr\"odinger operators associated to strictly ergodic dynamical systems is shown to coincide with the set of zeros of the Lyapunov exponent if and only if the Lyapunov exponent exists uniformly. This is used to obtain Cantor spectrum of zero Lebesgue measure for all aperiodic subshifts with uniform positive weights. This covers, in particular, all aperiodic subshifts arising from primitive substitutions including new examples as e.g. the Rudin-Shapiro substitution. Our investigation is not based on trace maps. Instead it relies on an Oseledec type theorem due to A. Furman and a uniform ergodic theorem due to the author.