一维准晶Lebesgue测度零的奇异谱
Singular spectrum of Lebesgue measure zero for one-dimensional quasicrystals
摘要：
证明了严格遍历动力系统的一维离散薛定谔算子的谱与李雅普诺夫指数的零点集一致的充要条件是李雅普诺夫指数一致存在.这是用来获得的Cantor谱的零Lebesgue测度的所有非周期子移位具有一致的正权重。这涵盖了，特别是，所有的非周期子移位所产生的原始替代包括新的例子，例如鲁丁-夏皮罗替代。我们的调查不是基于痕迹地图。相反，它依赖于A. Furman和作者的一个一致遍历定理。
英文摘要：
The spectrum of one-dimensional discrete Schrödinger 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
