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

Abstract

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

Metrics

Item Actions

Export

You can export this page using these formats Digital Object Identifier - DOI

About

• Item ORO ID
• 52951
• Item Type
• Journal Item
• ISSN
• 1573-0530
• Keywords
• substitution dynamical systems; renormalisation; Spectral theory; diffraction; Lyapunov exponents; Mahler measure
• Academic Unit or School
• Faculty of Science, Technology, Engineering and Mathematics (STEM)
  Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
• Copyright Holders
• © 2018 Springer Science+Business Media B.V.
• Related URLs
• • http://rdcu.be/ET1I(Other)
• Depositing User
• Uwe Grimm