论文标题
Schrödinger运算符的光谱特性与几乎最小的替代系统相关
Spectral properties of Schrödinger operators associated to almost minimal substitution systems
论文作者
论文摘要
我们研究了与二进制字母上某个非主要取代家族相关的ergodicSchrödinger运算符的光谱特性。相应的子迁移提供了超出最小性，独特的牙齿和线性复杂性的动力系统的示例。在某些参数区域中，我们自然是在无限的厄运措施的设置中。几乎确定的频谱是单数的，并且包含一个间隔。排除特征值的一些标准已充分表征，包括存在强烈的倾向序列。我们的许多结构见解都依赖于返回单词分解，在不均匀的复发序列的背景下。我们引入了一个相关的诱导系统，该系统偶联到里程表。
We study the spectral properties of ergodic Schrödinger operators that are associated to a certain family of non-primitive substitutions on a binary alphabet. The corresponding subshifts provide examples of dynamical systems that go beyond minimality, unique ergodicity and linear complexity. In some parameter region, we are naturally in the setting of an infinite ergodic measure. The almost sure spectrum is singular and contains an interval. Some criteria for the exclusion of eigenvalues are fully characterized, including the existence of strongly palindromic sequences. Many of our structural insights rely on return word decompositions in the context of non-uniformly recurrent sequences. We introduce an associated induced system that is conjugate to an odometer.
