کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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4657983 | 1633074 | 2016 | 24 صفحه PDF | دانلود رایگان |
This article presents, in an illustrative fashion, a first step towards an extension of the spectral theory of constant length substitutions. Our starting point is the general observation that the symbolic picture (as defined by the substitution rule) and its geometric counterpart with natural prototile sizes (as defined by the induced inflation rule) may differ considerably. On the geometric side, an aperiodic inflation system possesses a set of exact renormalisation relations for its pair correlation coefficients. Here, we derive these relations for some paradigmatic examples and infer various spectral consequences. In particular, we consider the Fibonacci chain, revisit the Thue–Morse and the Rudin–Shapiro system, and finally analyse a twisted extension of the silver mean chain with mixed singular spectrum.
Journal: Topology and its Applications - Volume 205, 1 June 2016, Pages 4–27