Squirals and beyond: substitution tilings with singular continuous spectrum

DOI10.1017/etds.2012.191zbMath1315.37015arXiv1205.1384OpenAlexW3106501385MaRDI QIDQ2925256

Michael Baake, Uwe Grimm

Publication date: 21 October 2014

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1205.1384

zbMATH Keywords

pure point spectrummixed spectrumsubstitution systemaperiodic tilingsingular continuous spectrumdynamical spectrumdiffraction spectrum

Mathematics Subject Classification ID

Related Items (21)

Pair correlations of aperiodic inflation rules via renormalisation: some interesting examples ⋮ On substitution automorphisms with pure singular spectrum ⋮ Spectral theory of spin substitutions ⋮ Spectral properties of substitutions on compact alphabets ⋮ Self-similarity and spectral theory: on the spectrum of substitutions ⋮ Why do (weak) Meyer sets diffract? ⋮ Tempered distributions with translation bounded measure as Fourier transform and the generalized Eberlein decomposition ⋮ Introduction to Hierarchical Tiling Dynamical Systems ⋮ Renormalisation of Pair Correlations and Their Fourier Transforms for Primitive Block Substitutions ⋮ Binary Constant-Length Substitutions and Mahler Measures of Borwein Polynomials ⋮ A natural probability measure derived from Stern’s diatomic sequence ⋮ Spectral notions of aperiodic order ⋮ Spectral theory of substitutions ⋮ Geometric properties of a binary non-Pisot inflation and absence of absolutely continuous diffraction ⋮ On the Fourier analysis of measures with Meyer set support ⋮ Pure point/continuous decomposition of translation-bounded measures and diffraction ⋮ Extended symmetry groups of multidimensional subshifts with hierarchical structure ⋮ A note on measures vanishing at infinity ⋮ Singular substitutions of constant length ⋮ Renormalisation of pair correlation measures for primitive inflation rules and absence of absolutely continuous diffraction ⋮ Spectral and arithmetic structures in aperiodic order

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the notions of symmetry and aperiodicity for Delone sets
• On the table and the chair
• Computing modular coincidences for substitution tilings and point sets
• Substitution dynamical systems. Spectral analysis
• Diffraction of stochastic point sets: Explicitly computable examples
• Planar dynamical systems with pure Lebesgue diffraction spectrum
• Consequences of pure point diffraction spectra for multiset substitution systems
• Pure point dynamical and diffraction spectra
• On diffraction by aperiodic structures
• Multidimensional constant-length substitution sequences
• Spectral and topological properties of a family of generalised Thue-Morse sequences
• Multifractal analysis in reciprocal space and the nature of the Fourier transform of self-similar structures
• Characterization of model sets by dynamical systems
• The singular continuous diffraction measure of the Thue–Morse chain
• Linearly repetitive Delone systems have a finite number of nonperiodic Delone system factors
• The spectrum of dynamical systems arising from substitutions of constant length
• Dynamics of self-similar tilings
• Automatic Sequences
• On the dimensions of the spectral measure of symmetric binary substitutions
• Repetitive Delone sets and quasicrystals
• Dynamical systems on translation bounded measures: pure point dynamical and diffraction spectra
• Diffraction of Weighted Lattice Subsets
• Generalized Morse sequences
• Lattice substitution systems and model sets

This page was built for publication: Squirals and beyond: substitution tilings with singular continuous spectrum