论文标题
连接了双倍地图模型的几乎确定的必需频谱
The Almost Sure Essential Spectrum of the Doubling Map Model is Connected
论文作者
论文摘要
我们考虑在半线上使用离散的schrödinger运算符，其势能由倍增图和连续采样函数产生。我们表明，这些操作员的基本频谱始终是连接的。通过计算与标准螺线管的悬浮液相关的schwartzman同构范围的亚组获得的结果，从而通过悬浮液的悬浮液来悬浮，然后表明该亚组表征了频谱的拓扑结构。
We consider discrete Schrödinger operators on the half line with potentials generated by the doubling map and continuous sampling functions. We show that the essential spectrum of these operators is always connected. This result is obtained by computing the subgroup of the range of the Schwartzman homomorphism associated with homotopy classes of continuous maps on the suspension of the standard solenoid that factor through the suspension of the doubling map and then showing that this subgroup characterizes the topological structure of the spectrum.
