Examples of substitution systems and their factors

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Abstract

The theory of substitution sequences and their higher-dimensional analogues is intimately connected with symbolic dynamics. By systematically studying the factors (in the sense of dynamical systems theory) of a substitution dynamical system, one can reach a better understanding of spectral and topological properties. We illustrate this point of view by means of some characteristic examples, including a rather universal substitution in one dimension as well as the squiral and the table tilings of the plane.

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Pure Point Dynamical and Diffraction Spectra

Jeong-Yup Lee, Boris Solomyak, Robert V. Moody (2009)

We show that for multi-colored Delone point sets with finite local complexity and uniform cluster frequencies the notions of pure point diffraction and pure point dynamical spectrum are equivalent.

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Dynamical systems on translation bounded measures: Pure point dynamical and diffraction spectra

Michael Baake, Daniel Lenz (2003)

Certain topological dynamical systems are considered that arise from actions of \(\sigma\)-compact locally compact Abelian groups on compact spaces of translation bounded measures. Such a measure dynamical system is shown to have pure point dynamical spectrum if and only if its diffraction spectrum is pure point.