M. Baake
Planar dynamical systems with pure Lebesgue diffraction spectrum
Baake, M.; Ward, T.
Authors
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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