Affiliation:
1. Faculty of Mathematics Technion Israel Institute of Technology Technion City Haifa 3200003 Israel
Abstract
AbstractPeriodic 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.
Funder
Deutsche Forschungsgemeinschaft
Israel Science Foundation
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