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

Baake M, Frank NP, Grim U, Robinson, E. Arthur J (2019)
STUDIA MATHEMATICA 247(2): 109-154.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Baake, MichaelUniBi; Frank, Natalie Priebe; Grim, Uwe; Robinson, E. Arthur, Jr.
Abstract / Bemerkung
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 renormalisation 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.
Erscheinungsjahr
2019
Zeitschriftentitel
STUDIA MATHEMATICA
Band
247
Ausgabe
2
Seite(n)
109-154
ISSN
0039-3223
eISSN
1730-6337
Page URI
https://pub.uni-bielefeld.de/record/2934631

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Baake M, Frank NP, Grim U, Robinson, E. Arthur J. Geometric properties of a binary non-Pisot inflation and absence of absolutely continuous diffraction. STUDIA MATHEMATICA. 2019;247(2):109-154.
Baake, M., Frank, N. P., Grim, U., & Robinson, E. Arthur, J. (2019). Geometric properties of a binary non-Pisot inflation and absence of absolutely continuous diffraction. STUDIA MATHEMATICA, 247(2), 109-154. doi:10.4064/sm170613-10-3
Baake, M., Frank, N. P., Grim, U., and Robinson, E. Arthur, J. (2019). Geometric properties of a binary non-Pisot inflation and absence of absolutely continuous diffraction. STUDIA MATHEMATICA 247, 109-154.
Baake, M., et al., 2019. Geometric properties of a binary non-Pisot inflation and absence of absolutely continuous diffraction. STUDIA MATHEMATICA, 247(2), p 109-154.
M. Baake, et al., “Geometric properties of a binary non-Pisot inflation and absence of absolutely continuous diffraction”, STUDIA MATHEMATICA, vol. 247, 2019, pp. 109-154.
Baake, M., Frank, N.P., Grim, U., Robinson, E. Arthur, J.: Geometric properties of a binary non-Pisot inflation and absence of absolutely continuous diffraction. STUDIA MATHEMATICA. 247, 109-154 (2019).
Baake, Michael, Frank, Natalie Priebe, Grim, Uwe, and Robinson, E. Arthur, Jr. “Geometric properties of a binary non-Pisot inflation and absence of absolutely continuous diffraction”. STUDIA MATHEMATICA 247.2 (2019): 109-154.

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