标题： 一维符号替换系统的近似 显示英文标题

标题： Approximations of symbolic substitution systems in one dimension

摘要： 准晶体的周期逼近是分析由准晶体产生的薛定谔算子谱的强大工具，鉴于已知的周期晶体理论。 即，我们寻找其谱可以逼近准晶体极限算子谱的周期算子。 这自然导致研究底层动力系统的收敛性。 我们研究基于一维替换的动力系统。 我们首先找到用于近似替换动力系统的自然候选动力子系统。 随后，我们提供它们收敛性的表征，并给出收敛速率的估计。 我们将所提出的理论应用于一些指导性例子。 显示英文摘要

摘要： Periodic approximations of quasicrystals are a powerful tool in analyzing spectra of Schr\"odinger 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.