On the spectrum of the Thue-Morse quasicrystal and the rarefaction phenomenon

DOI10.5802/jtnb.645zbMath1205.11031arXiv0811.4361OpenAlexW1998169274MaRDI QIDQ1026979

Jean-Louis Verger-Gaugry, Jean-Pierre Gazeau

Publication date: 30 June 2009

Published in: Journal de Théorie des Nombres de Bordeaux (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0811.4361

zbMATH Keywords

spectrumThue-Morse sequencequasicrystalsum of digitssingular continuous measurerarefied sums

Mathematics Subject Classification ID

Radix representation; digital problems (11A63) Automata sequences (11B85) Quasicrystals and aperiodic tilings in discrete geometry (52C23)

Related Items (2)

Coquet-type formulas for the rarefied weighted Thue-Morse sequence ⋮ Relating diffraction and spectral data of aperiodic tilings: towards a Bloch theorem

Cites Work

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• A summation formula related to the binary digits
• Substitution dynamical systems - spectral analysis
• The fractal structure of rarefied sums of the Thue-Morse sequence
• Étude de quelques propriétés des produits de Riesz
• On Artin's conjecture and Euclid's algorithm in global fields
• Fractal digital sums and codes
• Fractal behaviour of diffraction pattern of Thue-Morse sequence.
• Almost periodic measures and long-range order in Meyer sets
• On diffraction by aperiodic structures
• Sign-changes of the Thue-Morse fractal function and Dirichlet \(L\)-series
• Meyer's concept of quasicrystal and quasiregular sets
• Scaling properties of a structure intermediate between quasiperiodic and random.
• Diffraction spectra of weighted Delone sets on beta-lattices with beta a quadratic unitary Pisot number
• On the distribution of values of sums of the type \(\sum f(2^kt)\)
• Class Groups of Number Fields: Numerical Heuristics
• Multifractal analysis in reciprocal space and the nature of the Fourier transform of self-similar structures
• WHICH DISTRIBUTIONS OF MATTER DIFFRACT ? AN INITIAL INVESTIGATION
• Completely q-multiplicative functions: the Mellin transform approach
• Rarified sums of the Thue-Morse sequence
• A proof of the dynamical version of the Bombieri–Taylor conjecture
• Multifractal analysis of the spectral measure of the Thue–Morse sequence: a periodic orbit approach
• Sur les nombres qui ont des propriétés additives et multiplicatives données
• On the Number of Binary Digits in a Multiple of Three
• A note on the parity of the sum-of-digits function

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