Spectral and arithmetic structures in aperiodic order
Michael BaakeUniversität Bielefeld, Germany
Franz GählerUniversität Bielefeld, Germany
Christian HuckUniversität Bielefeld, Germany
Peter ZeinerXiamen University Malaysia, Sepang, Selangor, Malaysia
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Systems with aperiodic order can display a variety of arithmetic, combinatorial and spectral phenomena, some of which are reviewed and discussed here. At the same time, the underlying compact tiling spaces can be compared via their topological and spectral invariants. The latter are explicitly computable for substitution systems and provide an important tool for their classification.