Planar Dynamical Systems with Pure Lebesgue Diffraction Spectrum

Baake M, Ward T (2010)
JOURNAL OF STATISTICAL PHYSICS 140(1): 90-102.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
We examine the diffraction properties of lattice dynamical systems of algebraic origin. It is well-known that diverse dynamical properties occur within this class. These include different orders of mixing (or higher-order correlations), the presence or absence of measure rigidity (restrictions on the set of possible shift-invariant ergodic measures to being those of algebraic origin), and different entropy ranks (which may be viewed as the maximal spatial dimension in which the system resembles an i.i.d. process). Despite these differences, it is shown that the resulting diffraction spectra are essentially indistinguishable, thus raising further difficulties for the inverse problem of structure determination from diffraction spectra. Some of them may be resolved on the level of higher-order correlation functions, which we also briefly compare.
Stichworte
Mathematical diffraction theory; Pure Lebesgue spectrum; Dynamical systems of algebraic origin
Erscheinungsjahr
2010
Zeitschriftentitel
JOURNAL OF STATISTICAL PHYSICS
Band
140
Ausgabe
1
Seite(n)
90-102
ISSN
0022-4715
Page URI
https://pub.uni-bielefeld.de/record/1795681

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Baake M, Ward T. Planar Dynamical Systems with Pure Lebesgue Diffraction Spectrum. JOURNAL OF STATISTICAL PHYSICS. 2010;140(1):90-102.
Baake, M., & Ward, T. (2010). Planar Dynamical Systems with Pure Lebesgue Diffraction Spectrum. JOURNAL OF STATISTICAL PHYSICS, 140(1), 90-102. https://doi.org/10.1007/s10955-010-9984-x
Baake, M., and Ward, T. (2010). Planar Dynamical Systems with Pure Lebesgue Diffraction Spectrum. JOURNAL OF STATISTICAL PHYSICS 140, 90-102.
Baake, M., & Ward, T., 2010. Planar Dynamical Systems with Pure Lebesgue Diffraction Spectrum. JOURNAL OF STATISTICAL PHYSICS, 140(1), p 90-102.
M. Baake and T. Ward, “Planar Dynamical Systems with Pure Lebesgue Diffraction Spectrum”, JOURNAL OF STATISTICAL PHYSICS, vol. 140, 2010, pp. 90-102.
Baake, M., Ward, T.: Planar Dynamical Systems with Pure Lebesgue Diffraction Spectrum. JOURNAL OF STATISTICAL PHYSICS. 140, 90-102 (2010).
Baake, Michael, and Ward, Tom. “Planar Dynamical Systems with Pure Lebesgue Diffraction Spectrum”. JOURNAL OF STATISTICAL PHYSICS 140.1 (2010): 90-102.

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