Hierarchical structures in Sturmian dynamical systems

DOI10.1016/S0304-3975(03)00207-XzbMath1027.37006arXivmath/0005061MaRDI QIDQ1401381

Daniel H. Lenz

Publication date: 17 August 2003

Published in: Theoretical Computer Science (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0005061

zbMATH Keywords

WeightsQuasicrystalsHierarchiesLattice gas modelsSturmian systemsUniform ergodic theorems

Mathematics Subject Classification ID

Combinatorics on words (68R15) Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics) (37N20) Ergodic theorems, spectral theory, Markov operators (37A30) Symbolic dynamics (37B10) Quasicrystals and aperiodic tilings in discrete geometry (52C23)

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Powers in Sturmian sequences ⋮ A characterization of subshifts with bounded powers ⋮ A characterization of linearly repetitive cut and project sets ⋮ UNIFORM ERGODIC THEOREMS ON APERIODIC LINEARLY REPETITIVE TILINGS AND APPLICATIONS ⋮ An ergodic theorem for Delone dynamical systems and existence of the integrated density of states ⋮ Uniform spectral properties of one-dimensional quasicrystals. IV. Quasi-Sturmian potentials

Cites Work

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• Quasicrystallographic tilings
• On the number of factors of Sturmian words
• The spectrum of a quasiperiodic Schrödinger operator
• Substitution dynamical systems - spectral analysis
• Power law growth for the resistance in the Fibonacci model
• Complexity for finite factors of infinite sequences
• The index of Sturmian sequences
• A characterization of substitutive sequences using return words
• Sturmian words and words with a critical exponent
• Uniform spectral properties of one-dimensional quasicrystals. III: \(\alpha\)-continuity.
• Uniform spectral properties of one-dimensional quasicrystals. II: The Lyapunov exponent.
• Uniform spectral properties of one-dimensional quasicrystals. I: Absence of eigenvalues
• Spectral properties of one dimensional quasi-crystals
• Singular spectrum of Lebesgue measure zero for one-dimensional quasicrystals
• An ergodic theorem for Delone dynamical systems and existence of the integrated density of states
• Some remarks on discrete aperiodic Schrödinger operators
• Return words in Sturmian and episturmian words
• Substitutional dynamical systems, Bratteli diagrams and dimension groups
• LATTICE GAS MODELS ON SELF-SIMILAR APERIODIC TILINGS
• Descriptions of the Characteristic Sequence of an Irrational
• Linearly recurrent subshifts have a finite number of non-periodic subshift factors
• Uniform ergodic theorems on subshifts over a finite alphabet
• Absence of point spectrum for a class of discrete Schrödinger operators with quasiperiodic potential
• Sturmian Minimal Sets
• A characterization of Sturmian words by return words
• Fractional powers in Sturmian words