Pure Point Dynamical and Diffraction Spectra

Abstract

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.

16 pages

References in corpus (1)

• Weighted Dirac combs with pure point diffraction

Cited by in corpus (57)

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• Pure point diffraction implies zero entropy for Delone sets with uniform cluster frequencies
• Mean sensitive, mean equicontinuous and almost periodic functions for dynamical systems
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• Computing modular coincidences
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• Dynamical properties of almost repetitive Delone sets
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• Hexagonal inflation tilings and planar monotiles
• Ergodicity and dynamical localization for Delone-Anderson operators
• Rokhlin dimension for flows
• Spectral analysis of a family of binary inflation rules
• Extinctions and Correlations for Uniformly Discrete Point Processes with Pure Point Dynamical Spectra
• Examples of substitution systems and their factors
• Self affine Delone sets and deviation phenomena
• On norm almost periodic measures
• Rapid convergence to frequency for Substitution Tilings of the Plane
• Pure point spectrum for dynamical systems and mean almost periodicity
• Random colourings of aperiodic graphs: Ergodic and spectral properties
• Close-packed dimers on the line: diffraction versus dynamical spectrum
• Ellis enveloping semigroup for almost canonical model sets of an Euclidean space
• Renormalisation of pair correlations and their Fourier transforms for primitive block substitutions
• Fourier transform of Rauzy fractals and point spectrum of 1D Pisot inflation tilings
• Lyapunov exponents for binary substitutions of constant length
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• Algorithm for determining pure pointedness of self-affine tilings
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• An aperiodic tile with edge-to-edge orientational matching rules
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• Dynamics and topology of the Hat family of tilings
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• Aperiodicity in equilibrium systems: Between order and disorder
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