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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 (In Press).

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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: 27 Jun 2018 08:22
URI: http://oro.open.ac.uk/id/eprint/54848
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