Pure point dynamical and diffraction spectra

DOI10.1007/s00023-002-8646-1zbMath1025.37004arXiv0910.4809OpenAlexW2076355659MaRDI QIDQ1854633

B. M. Solomyak, Robert V. Moody, Jeong-Yup Lee

Publication date: 3 December 2003

Published in: Annales Henri Poincaré (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0910.4809

zbMATH Keywords

spectral theorems pure point diffraction multicolored Delone point sets pure point dynamical spectrum uniform cluster frequencies

Mathematics Subject Classification ID

Statistical mechanics of crystals (82D25) Ergodic theorems, spectral theory, Markov operators (37A30) Smooth ergodic theory, invariant measures for smooth dynamical systems (37C40) Quasicrystals and aperiodic tilings in discrete geometry (52C23)

Related Items (80)

Amorphic complexity of group actions with applications to quasicrystals ⋮ Tower systems for linearly repetitive Delone sets ⋮ Pair correlations of aperiodic inflation rules via renormalisation: some interesting examples ⋮ Geometrical and spectral properties of Pisot substitutions ⋮ Inflations of self-affine tilings are integral algebraic Perron ⋮ Continuity of eigenfunctions of uniquely ergodic dynamical systems and intensity of Bragg peaks ⋮ Weighted Dirac combs with pure point diffraction ⋮ Pure point diffraction and cut and project schemes for measures: the smooth case ⋮ Discrete quasiperiodic sets with predefined local structure ⋮ Diffraction of compatible random substitutions in one dimension ⋮ Extinctions and correlations for uniformly discrete point processes with pure point dynamical spectra ⋮ Dynamical versus diffraction spectrum for structures with finite local complexity ⋮ Squirals and beyond: substitution tilings with singular continuous spectrum ⋮ Hexagonal inflation tilings and planar monotiles ⋮ Taylor-Socolar hexagonal tilings as model sets ⋮ Cut and project sets with polytopal window II: linear repetitivity ⋮ Dynamical properties of almost repetitive Delone sets ⋮ Spectral theory of spin substitutions ⋮ Fourier transformable measures with weak Meyer set support and their lift to the cut-and-project scheme ⋮ Spectral properties of substitutions on compact alphabets ⋮ On substitution tilings and Delone sets without finite local complexity ⋮ AN APERIODIC TILE WITH EDGE-TO-EDGE ORIENTATIONAL MATCHING RULES ⋮ Algorithm for determining pure pointedness of self-affine tilings ⋮ Delone dynamical systems and spectral convergence ⋮ Pure point spectrum for dynamical systems and mean, Besicovitch and Weyl almost periodicity ⋮ Lyapunov exponents for binary substitutions of constant length ⋮ Stationary processes and pure point diffraction ⋮ Aperiodic and linearly repetitive Lorentz gases of finite horizon are not exponentially mixing ⋮ An ultrametric state space with a dense discrete overlap distribution: paperfolding sequences ⋮ Gabor frames for quasicrystals, \(K\)-theory, and twisted gap labeling ⋮ Rapid convergence to frequency for substitution tilings of the plane ⋮ UNIFORM ERGODIC THEOREMS ON APERIODIC LINEARLY REPETITIVE TILINGS AND APPLICATIONS ⋮ PV cohomology of the pinwheel tilings, their integer group of coinvariants and gap-labeling ⋮ Fourier transform of Rauzy fractals and point spectrum of 1D Pisot inflation tilings ⋮ The computation of overlap coincidence in Taylor-Socolar substitution tiling ⋮ Delone Sets and Dynamical Systems ⋮ Introduction to Hierarchical Tiling Dynamical Systems ⋮ Renormalisation of Pair Correlations and Their Fourier Transforms for Primitive Block Substitutions ⋮ Spectral structures and topological methods in mathematical quasicrystals. Abstracts from the workshop held October 1--7, 2017 ⋮ Brillouin zone labelling for quasicrystals ⋮ On weakly almost periodic measures ⋮ On norm almost periodic measures ⋮ Cut and project sets with polytopal window I: Complexity ⋮ Inductive rotation tilings ⋮ Ellis enveloping semigroup for almost canonical model sets of an Euclidean space ⋮ Self affine Delone sets and deviation phenomena ⋮ Translation numbers for a class of maps on the dynamical systems arising from quasicrystals in the real line ⋮ Pure point diffraction implies zero entropy for Delone sets with uniform cluster frequencies ⋮ Spectral notions of aperiodic order ⋮ Dynamics on the graph of the torus parametrization ⋮ Spectral theory of substitutions ⋮ On weak model sets of extremal density ⋮ The cohomological equation over dynamical systems arising from Delone sets ⋮ Substitution Delone sets with pure point spectrum are inter-model sets ⋮ An ergodic theorem for Delone dynamical systems and existence of the integrated density of states ⋮ A primer of substitution tilings of the Euclidean plane ⋮ Self-dual tilings with respect to star-duality ⋮ Mean sensitive, mean equicontinuous and almost periodic functions for dynamical systems ⋮ Rokhlin dimension for flows ⋮ Homological Pisot substitutions and exact regularity ⋮ Pure point diffractive substitution Delone sets have the Meyer property ⋮ Dworkin's argument revisited: Point processes, dynamics, diffraction, and correlations ⋮ Close-packed dimers on the line: diffraction versus dynamical spectrum ⋮ Traces of random operators associated with self-affine Delone sets and Shubin's formula ⋮ Spectral analysis of a family of binary inflation rules ⋮ Pure point spectrum for measure dynamical systems on locally compact Abelian groups ⋮ Pure point/continuous decomposition of translation-bounded measures and diffraction ⋮ Substitution tilings with statistical circular symmetry ⋮ Deforming Meyer sets ⋮ Geometry of the common dynamics of flipped Pisot substitutions ⋮ A note on measures vanishing at infinity ⋮ Symmetric Intersections of Rauzy Fractals ⋮ On the symmetric intersection of Rauzy fractals associated with the k-bonacci substitution ⋮ Renormalisation of pair correlation measures for primitive inflation rules and absence of absolutely continuous diffraction ⋮ Spectral and arithmetic structures in aperiodic order ⋮ Quasicrystals and almost periodicity ⋮ Irregular model sets and tame dynamics ⋮ Factors of Pisot tiling spaces and the Coincidence Rank Conjecture ⋮ Spectral and topological properties of a family of generalised Thue-Morse sequences ⋮ An autocorrelation and a discrete spectrum for dynamical systems on metric spaces

This page was built for publication: Pure point dynamical and diffraction spectra