Spectral and arithmetic structures in aperiodic order

Topological entropy (37B40) Algebraic ergodic theory, cocycles, orbit equivalence, ergodic equivalence relations (37A20) Quasicrystals and aperiodic tilings in discrete geometry (52C23) Tiling dynamics (37B52) Dynamics in general topological spaces (37B02)

Cites Work

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Pair correlations of aperiodic inflation rules via renormalisation: some interesting examples
Diffraction of random noble means words
Ergodic properties of visible lattice points
On weak model sets of extremal density
On the entropy of a family of random substitutions
Pure point spectrum for measure dynamical systems on locally compact Abelian groups
On pattern entropy of weak model sets
Quasiperiodicity and randomness in tilings of the plane
Deformation of Delone dynamical systems and pure point diffraction
Substitution dynamical systems. Spectral analysis
Arithmétique des algèbres de quaternions
Diffraction from visible lattice points and $k$th power free integers
Pure point dynamical and diffraction spectra
On diffraction by aperiodic structures
Integral cohomology of rational projection method patterns
Pure point diffraction and cut and project schemes for measures: the smooth case
Entropy and diffraction of the $k$-free points in $n$-dimensional lattices
Coincidence rotations of the root lattice $A_4$
Multidimensional constant-length substitution sequences
The coincidence problem for shifted lattices and crystallographic point packings
Spectral and topological properties of a family of generalised Thue-Morse sequences
Squirals and beyond: substitution tilings with singular continuous spectrum
Well-rounded sublattices of planar lattices
Similar Sublattices of Planar Lattices
Similarity and Coincidence Isometries for Modules
Dynamical versus diffraction spectrum for structures with finite local complexity
Characterization of model sets by dynamical systems
The torus parametrization of quasiperiodic LI-classes
Topological invariants for substitution tilings and their associated $C^\ast$-algebras
Quasicrystals and icosians
A Guide to the Symmetry Structure of Quasiperiodic Tiling Classes
Dynamics of self-similar tilings
Substitution sequences in \mathbb{Z}^{d} with a non-simple Lebesgue component in the spectrum
Similarity Submodules and Root Systems in Four Dimensions
Uniform Distribution in Model Sets
On weakly almost periodic measures
Dynamics on the graph of the torus parametrization
Spectral theory of substitutions
Dynamical systems on translation bounded measures: pure point dynamical and diffraction spectra
Approximations diophantiennes et problèmes additifs dans les groupes abéliens localement compacts
Weighted Dirac combs with pure point diffraction
Geometric Enumeration Problems for Lattices and Embedded ℤ-Modules
Almost Periodic Pure Point Measures
Factors of Pisot tiling spaces and the Coincidence Rank Conjecture
Examples of substitution systems and their factors
Ergodic Theory

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