Asymptotic behavior of beta-integers

DOI10.1007/s11005-008-0241-zzbMath1185.11063arXiv0802.2992OpenAlexW2127559076MaRDI QIDQ1024851

L'ubomíra Balková, Edita Pelantová, Jean-Pierre Gazeau

Publication date: 17 June 2009

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0802.2992

zbMATH Keywords

asymptotic behaviorquasicrystalsbeta-numerationbeta-integersaperiodic structure

Mathematics Subject Classification ID

Density, gaps, topology (11B05) Symbolic dynamics (37B10) PV-numbers and generalizations; other special algebraic numbers; Mahler measure (11R06) Quasicrystals and aperiodic tilings in discrete geometry (52C23)

Related Items (7)

On the structure of (−β)-integers ⋮ Arithmetics in numeration systems with negative quadratic base ⋮ Hausdorff dimension of some sets in the theory of continued beta-fractions and its generalized continued fractions ⋮ Metric theorems for continued \(\beta\)-fractions ⋮ Lattice bounded distance equivalence for 1D Delone sets with finite local complexity ⋮ Repetitions in beta-integers ⋮ Noncommutative reading of the complex plane through Delone sequences

Cites Work

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• Diffraction spectra of weighted Delone sets on beta-lattices with beta a quadratic unitary Pisot number
• Representations for real numbers and their ergodic properties
• On theβ-expansions of real numbers
• Beta-integers as natural counting systems for quasicrystals
• On beta expansions for Pisot numbers

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