The Open UniversitySkip to content

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.

Full text available as:
PDF (Accepted Manuscript) - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
Download (312kB) | Preview
DOI (Digital Object Identifier) Link:
Google Scholar: Look up in Google Scholar


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.

Item Type: Journal Item
Copyright Holders: 2018 Springer Science+Business Media B.V.
ISSN: 1573-0530
Keywords: substitution dynamical systems; renormalisation; Spectral theory; diffraction; Lyapunov exponents; Mahler measure
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
Related URLs:
Item ID: 52951
Depositing User: Uwe Grimm
Date Deposited: 24 Jan 2018 16:02
Last Modified: 06 Jul 2020 06:56
Share this page:


Altmetrics from Altmetric

Citations from Dimensions

Download history for this item

These details should be considered as only a guide to the number of downloads performed manually. Algorithmic methods have been applied in an attempt to remove automated downloads from the displayed statistics but no guarantee can be made as to the accuracy of the figures.

Actions (login may be required)

Policies | Disclaimer

© The Open University   contact the OU