Geometric properties of a binary non-Pisot inflation and absence of absolutely continuous diffraction

DOI10.4064/sm170613-10-3zbMath1419.37017arXiv1706.03976OpenAlexW2626831117WikidataQ128887992 ScholiaQ128887992MaRDI QIDQ5742245

Michael Baake, Natalie Priebe Frank, E. Arthur jun. Robinson, Uwe Grimm

Publication date: 13 May 2019

Published in: Studia Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1706.03976

zbMATH Keywords

Lyapunov exponentssingular spectrumtiling dynamicsnon-Pisot substitutions

Mathematics Subject Classification ID

Related Items (16)

On substitution automorphisms with pure singular spectrum ⋮ Spectral theory of spin substitutions ⋮ Self-similarity and spectral theory: on the spectrum of substitutions ⋮ Lyapunov exponents for binary substitutions of constant length ⋮ Uniformly distributed orbits in \(\mathbb{T}^d\) and singular substitution dynamical systems ⋮ Fourier transform of Rauzy fractals and point spectrum of 1D Pisot inflation tilings ⋮ 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 ⋮ Binary Constant-Length Substitutions and Mahler Measures of Borwein Polynomials ⋮ A spectral cocycle for substitution systems and translation flows ⋮ Spectral analysis of a family of binary inflation rules ⋮ Three variations on a theme by Fibonacci ⋮ Renormalisation for inflation tilings. I: General theory ⋮ Renormalisation for inflation tilings. II: Connections to number theory ⋮ Renormalisation of pair correlation measures for primitive inflation rules and absence of absolutely continuous diffraction

Uses Software

• SaddleDrop
• VINAS-P
• Genius
• StableBBasisNBM5
• Apart
• $Apart
• formConv
• reszeta.lib
• DALIA
• GADMM
• Z_LINEAR_K

Cites Work

• Continuity of eigenfunctions of uniquely ergodic dynamical systems and intensity of Bragg peaks
• Substitution dynamical systems. Spectral analysis
• Quasi-Monte Carlo algorithms for unbounded, weighted integration problems
• Squirals and beyond: substitution tilings with singular continuous spectrum
• Almost Periodic Measures and their Fourier Transforms
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• Unnamed Item

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