一维符号替换系统的逼近
Approximations of symbolic substitution systems in one dimension
AI总结：
该研究针对准晶体薛定谔算子谱分析需求，研究一维替换动力系统的周期逼近，给出逼近子系统候选、收敛性刻画与速率估计，并应用于示例，为准晶体相关算子谱分析提供工具。
摘要：
鉴于周期晶体的已有理论，准晶体的周期逼近是分析准晶体衍生的薛定谔算子谱的有力工具。具体而言，我们寻找其谱能逼近（准晶体的）极限算子谱的周期算子。这自然引出对底层动力系统收敛性的研究。我们研究基于一维替换的动力系统。首先找到用于逼近替换动力系统的动力子系统的自然候选对象，随后给出其收敛性的刻画，并提供收敛速率的估计。我们将所提出的理论应用于一些指导性示例。
英文摘要：
Periodic approximations of quasicrystals are a powerful tool in analyzing spectra of Schrödinger operators arising from quasicrystals, given the known theory for periodic crystals. Namely, we seek periodic operators whose spectra approximate the spectrum of the limiting operator (of the quasicrystal). This naturally leads to study the convergence of the underlying dynamical systems. We treat dynamical systems which are based on one-dimensional substitutions. We first find natural candidates of dynamical subsystems to approximate the substitution dynamical system. Subsequently, we offer a characterization of their convergence and provide estimates for the rate of convergence. We apply the proposed theory to some guiding examples.
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