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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.

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DOI (Digital Object Identifier) Link: https://doi.org/10.1007/s11005-018-1045-4
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Abstract

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)
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Item ID: 52951
Depositing User: Uwe Grimm
Date Deposited: 24 Jan 2018 16:02
Last Modified: 21 Jun 2018 11:26
URI: http://oro.open.ac.uk/id/eprint/52951
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