Planar dynamical systems with pure Lebesgue diffraction spectrum

Baake, Michael and Ward, Tom (2010) Planar dynamical systems with pure Lebesgue diffraction spectrum. Journal of Statistical Physics, 140 (1). pp. 90-102. ISSN 0022-4715

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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.

Item Type: Article
Faculty \ School: Faculty of Science > School of Mathematics
Related URLs:
Depositing User: Vishal Gautam
Date Deposited: 18 Mar 2011 14:48
Last Modified: 12 Jan 2024 01:21
DOI: 10.1007/s10955-010-9984-x

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