Spectral analysis of a family of binary inflation rules

Baake, Michael; Grimm, Uwe and Mañibo, Neil (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


The family of primitive binary substitutions defined by 1 ↦ 0 ↦ 01m 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.

Viewing alternatives

Download history


Public Attention

Altmetrics from Altmetric

Number of Citations

Citations from Dimensions

Item Actions