The Open UniversitySkip to content
 

Geometric properties of a binary non-Pisot inflation and absence of absolutely continuous diffraction

Baake, Michael; Frank, Natalie Priebe; Grimm, Uwe and Robinson, Jr., E. Arthur (2019). Geometric properties of a binary non-Pisot inflation and absence of absolutely continuous diffraction. Studia Mathematica, 247 pp. 109–154.

Full text available as:
[img]
Preview
PDF (Accepted Manuscript) - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
Download (562kB) | Preview
DOI (Digital Object Identifier) Link: https://doi.org/10.4064/sm170613-10-3
Google Scholar: Look up in Google Scholar

Abstract

One of the simplest non-Pisot substitution rules is investigated in its geometric version as a tiling with intervals of natural length as prototiles. Via a detailed renormalization analysis of the pair correlation functions, we show that the diffraction measure cannot comprise any absolutely continuous component. This implies that the diffraction, apart from a trivial Bragg peak at the origin, is purely singular continuous. En route, we derive various geometric and algebraic properties of the underlying Delone dynamical system, which we expect to be relevant in other such systems as well.

Item Type: Journal Item
Copyright Holders: 2018 Instytut Matematyczny PAN
ISSN: 0039-3223
Extra Information: 2010 Mathematics Subject Classification. Primary 37A30, 42A38, 37B50; Secondary 37H15, 52C23
Keywords: non-Pisot substitutions; tiling dynamics; singular spectrum; Lyapunov exponents
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
Item ID: 54848
Depositing User: Uwe Grimm
Date Deposited: 03 May 2018 10:07
Last Modified: 16 Jun 2020 05:19
URI: http://oro.open.ac.uk/id/eprint/54848
Share this page:

Metrics

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