Substitution sequences in \mathbb{Z}^{d} with a non-simple Lebesgue component in the spectrum

DOI10.1017/S0143385702001256zbMath1031.11009OpenAlexW2057063746MaRDI QIDQ4438713

Natalie Priebe Frank

Publication date: 9 December 2003

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

Full work available at URL: https://doi.org/10.1017/s0143385702001256

zbMATH Keywords

Hadamard matricesdynamical spectrumsubstitution sequencesRudin-Shapiro sequencesLebesgue spectral measure

Mathematics Subject Classification ID

Measure-preserving transformations (28D05) Symbolic dynamics (37B10) Automata sequences (11B85) Special sequences (11K31)

Related Items (21)

Pair correlations of aperiodic inflation rules via renormalisation: some interesting examples ⋮ On substitution automorphisms with pure singular spectrum ⋮ Substitution-based structures with absolutely continuous spectrum ⋮ Discrete correlations of order 2 of generalised Rudin-Shapiro sequences: a combinatorial approach ⋮ Rudin–Shapiro sequences along squares ⋮ Spectral theory of spin substitutions ⋮ Self-similarity and spectral theory: on the spectrum of substitutions ⋮ Lyapunov exponents for binary substitutions of constant length ⋮ Admissible reversing and extended symmetries for bijective substitutions ⋮ Monochromatic arithmetic progressions in automatic sequences with group structure ⋮ Uniformly distributed orbits in \(\mathbb{T}^d\) and singular substitution dynamical systems ⋮ On the modulus of continuity for spectral measures in substitution dynamics ⋮ Introduction to Hierarchical Tiling Dynamical Systems ⋮ Spectral theory of substitutions ⋮ Dworkin's argument revisited: Point processes, dynamics, diffraction, and correlations ⋮ Averages of automatic sequences ⋮ 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 ⋮ Multidimensional constant-length substitution sequences ⋮ Spectrum of a Rudin-Shapiro-like sequence

This page was built for publication: Substitution sequences in \mathbb{Z}^{d} with a non-simple Lebesgue component in the spectrum