论文标题
约翰逊 - 施瓦茨曼（Johnson-Schwartzman）的差距标签
Johnson-Schwartzman Gap Labelling for Ergodic Jacobi Matrices
论文作者
论文摘要
我们考虑两侧的雅各比矩阵，其系数是通过沿着紧凑型公制空间的同源物的轨道连续采样获得的。给定沿阵行的概率度量，我们研究了相关的几乎肯定光谱的拓扑结构。我们以约翰逊和施瓦茨曼的精神建立了一个差距标记定理。也就是说，我们表明，状态的集成密度占据频谱的差异必须属于基本动力学的可数施瓦茨曼组。这个结果是Alkorn和Zhang最近结果的自然伴侣，Alkorn和Zhang为雅各比矩阵的家庭建立了约翰逊型定理。
We consider two-sided Jacobi matrices whose coefficients are obtained by continuous sampling along the orbits of a homeomorphim of a compact metric space. Given an ergodic probability measure, we study the topological structure of the associated almost sure spectrum. We establish a gap labelling theorem in the spirit of Johnson and Schwartzman. That is, we show that the constant value the integrated density of states takes in a gap of the spectrum must belong to the countable Schwartzman group of the base dynamics. This result is a natural companion to a recent result of Alkorn and Zhang, which established a Johnson-type theorem for the families of Jacobi matrices in question.
