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The positions of the Bragg peaks in point set diffraction show up as eigenvalues of a dynamical system. Topological Bragg peaks arise from topological eigenvalues and determine the torus parametrisation of the point set. We will discuss how qualitative properties of the torus parametrisation characterise the point set.
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[6] M. Baake, U. Grimm, Aperiodic Order: A Mathematical Invitation, Cambridge University Press, Cambridge 2013
[7] R.V. Moody, in: The Mathematics of Long-Range Aperiodic Order, Ed. R.V. Moody, Kluwer 1997, p. 403