论文标题
$ \ mathrm {sl}的均匀性方面（2，\ Mathbb {r}）$ cocycles and申请给Schrödinger运营商，该操作员通过Boshernitzan subshifts定义了
Uniformity Aspects of $\mathrm{SL}(2,\mathbb{R})$ Cocycles and Applications to Schrödinger Operators Defined Over Boshernitzan Subshifts
论文作者
论文摘要
我们考虑连续$ \ mathrm {sl}（2，\ mathbb {r}）$在一般动态系统上有价值的旋转，并讨论各种统一性概念。特别是，我们提供了连续$ \ mathrm {sl}的统一单参数系列（2，\ m athbb {r}）$ cocycles as $g_Δ$ -sets。然后将这些结果应用于具有动态定义电势的Schrödinger运营商。如果通过满足Boshernitzan条件的子升级给出了基本动力学，我们表明，对于通用连续采样函数，相关的Schrödinger共生对所有能量都是均匀的，而在Aperiodic情况下，频谱是零Lebesgue Measure setor setor setor set of le lebesgue测度。
We consider continuous $\mathrm{SL}(2,\mathbb{R})$ valued cocycles over general dynamical systems and discuss a variety of uniformity notions. In particular, we provide a description of uniform one-parameter families of continuous $\mathrm{SL}(2,\mathbb{R})$ cocycles as $G_δ$-sets. These results are then applied to Schrödinger operators with dynamically defined potentials. In the case where the base dynamics is given by a subshift satisfying the Boshernitzan condition, we show that for a generic continuous sampling function, the associated Schrödinger cocycles are uniform for all energies and, in the aperiodic case, the spectrum is a Cantor set of zero Lebesgue measure.
