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Planar dynamical systems with pure Lebesgue diffraction spectrum

Baake, M.; Ward, T.

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Authors

M. Baake

T. Ward



Abstract

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.

Citation

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

Journal Article Type Article
Publication Date Jan 1, 2010
Deposit Date Oct 12, 2012
Publicly Available Date Mar 28, 2024
Journal Journal of Statistical Physics
Print ISSN 0022-4715
Electronic ISSN 1572-9613
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 140
Issue 1
Pages 90-102
DOI https://doi.org/10.1007/s10955-010-9984-x

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Copyright Statement
The original publication is available at www.springerlink.com




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