Pair correlations of aperiodic inflation rules via renormalisation: Some interesting examples

Baake M, Gähler F (2016)
TOPOLOGY AND ITS APPLICATIONS 205: 4-27.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
This article presents, in an illustrative fashion, a first step towards an extension of the spectral theory of constant length substitutions. Our starting point is the general observation that the symbolic picture (as defined by the substitution rule) and its geometric counterpart with natural prototile sizes (as defined by the induced inflation rule) may differ considerably. On the geometric side, an aperiodic inflation system possesses a set of exact renormalisation relations for its pair correlation coefficients. Here, we derive these relations for some paradigmatic examples and infer various spectral consequences. In particular, we consider the Fibonacci chain, revisit the Thue-Morse and the Rudin-Shapiro system, and finally analyse a twisted extension of the silver mean chain with mixed singular spectrum. (C) 2016 The Authors. Published by Elsevier B.V. All rights reserved.
Stichworte
Inflation rules; Correlations; Renormalisation; Spectra
Erscheinungsjahr
2016
Zeitschriftentitel
TOPOLOGY AND ITS APPLICATIONS
Band
205
Seite(n)
4-27
Konferenz
Pisot Conjecture Workshop
Konferenzort
Leiden, NETHERLANDS
ISSN
0166-8641
eISSN
1879-3207
Page URI
https://pub.uni-bielefeld.de/record/2917129

Zitieren

Baake M, Gähler F. Pair correlations of aperiodic inflation rules via renormalisation: Some interesting examples. TOPOLOGY AND ITS APPLICATIONS. 2016;205:4-27.
Baake, M., & Gähler, F. (2016). Pair correlations of aperiodic inflation rules via renormalisation: Some interesting examples. TOPOLOGY AND ITS APPLICATIONS, 205, 4-27. https://doi.org/10.1016/j.topol.2016.01.017
Baake, M., and Gähler, F. (2016). Pair correlations of aperiodic inflation rules via renormalisation: Some interesting examples. TOPOLOGY AND ITS APPLICATIONS 205, 4-27.
Baake, M., & Gähler, F., 2016. Pair correlations of aperiodic inflation rules via renormalisation: Some interesting examples. TOPOLOGY AND ITS APPLICATIONS, 205, p 4-27.
M. Baake and F. Gähler, “Pair correlations of aperiodic inflation rules via renormalisation: Some interesting examples”, TOPOLOGY AND ITS APPLICATIONS, vol. 205, 2016, pp. 4-27.
Baake, M., Gähler, F.: Pair correlations of aperiodic inflation rules via renormalisation: Some interesting examples. TOPOLOGY AND ITS APPLICATIONS. 205, 4-27 (2016).
Baake, Michael, and Gähler, Franz. “Pair correlations of aperiodic inflation rules via renormalisation: Some interesting examples”. TOPOLOGY AND ITS APPLICATIONS 205 (2016): 4-27.

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