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Spectral analysis of a family of binary inflation rules

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arxiv 1709.09083 v2 pith:JHM6KMNL submitted 2017-09-26 math.DS math-phmath.MP

Michael Baake (Bielefeld) , Uwe Grimm (Milton Keynes) , Neil Manibo (Bielefeld) This is my paper · ORCID
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Twisted cocycle for interval exchange transformations: Invariant structures and Lyapunov spectrum

    math.DS 2025-01 conditional novelty 8.0 of 10

    The twisted cocycle over interval exchange renormalizations has a symmetric Lyapunov spectrum with at least κ+1 zero exponents, and is fully degenerate for rotation-type permutations on their homology torus.

  2. Renormalisation techniques for inflation systems and some of their applications

    math.DS 2026-06 unverdicted novelty 2.0 of 10

    Reviews renormalisation techniques for inflation-generated tiling systems, applies them to exact diffraction computation for new monotiles, and uses them with Lyapunov exponents to analyze spectral properties.

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