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arXiv · 1709.09083

Spectral analysis of a family of binary inflation rules

Michael Baake·Uwe Grimm·Neil Manibo
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Abstract

The family of primitive binary substitutions defined by $1 \mapsto 0 \mapsto 0 1^m$ with $m\in\mathbb{N}$ 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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Michael Baake, Uwe Grimm, Neil Manibo. 2017-09-26. Spectral analysis of a family of binary inflation rules. https://doi.org/10.1007/s11005-018-1045-4

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