Spectral analysis of a family of binary inflation rules

Baake, Michael and (2018). Spectral analysis of a family of binary inflation rules. Letters in Mathematical Physics, 108(8) pp. 1783–1805.

DOI: https://doi.org/10.1007/s11005-018-1045-4

Abstract

The family of primitive binary substitutions defined by 1 ↦ 0 ↦ 01^m with integer m ∈ ℕ is investigated. The spectral type of the corresponding diffraction measure is analysed for its geometric realisation with prototiles (intervals) of natural length. Apart from the well-known Fibonacci inflation (m=1), the inflation rules either have integer inflation factors, but non-constant length, or are of non-Pisot type. We show that all of them have singular diffraction, either of pure point type or essentially singular continuous.

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