Geometry, dynamics, and arithmetic of $S$-adic shifts

DOI10.5802/aif.3273zbMath1433.37010arXiv1410.0331OpenAlexW3102426279MaRDI QIDQ2421943

Wolfgang Steiner, Valérie Berthé, Jörg M. Thuswaldner

Publication date: 18 June 2019

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1410.0331

zbMATH Keywords

Lyapunov exponentsPisot numberssymbolic dynamicscontinued fractionstilingsBrun algorithmsubstitutions$S$-adic shiftsArnoux-Rauzy algorithm

Mathematics Subject Classification ID

Fractals (28A80) Symbolic dynamics (37B10) Metric theory of continued fractions (11K50) Special sequences (11K31) Tiling dynamics (37B52) Relations between ergodic theory and harmonic analysis (37A46)

Related Items (14)

Rauzy induction of polygon partitions and toral \(\mathbb{Z}^2\)-rotations ⋮ Arnoux-Rauzy interval exchanges ⋮ On the dimension group of unimodular \(\mathcal{S}\)-adic subshifts ⋮ Decidability Problems for Self-induced Systems Generated by a Substitution ⋮ Low complexity subshifts have discrete spectrum ⋮ Multidimensional continued fractions and symbolic codings of toral translations ⋮ Generalizations of Sturmian sequences associated with \(\boldsymbol{N}\)-continued fraction algorithms ⋮ On triangular paperfolding patterns ⋮ S-adic Sequences: A Bridge Between Dynamics, Arithmetic, and Geometry ⋮ A spectral cocycle for substitution systems and translation flows ⋮ Hölder regularity for the spectrum of translation flows ⋮ Tilings from graph directed iterated function systems ⋮ Random substitution tilings and deviation phenomena ⋮ Markov partitions for toral \(\mathbb{Z}^2\)-rotations featuring Jeandel-Rao Wang shift and model sets

Cites Work

• Pure discrete spectrum for a class of one-dimensional substitution tiling systems
• The \(S\)-adic Pisot conjecture on two letters
• Finitely balanced sequences and plasticity of 1-dimensional tilings
• The geometry of non-unit Pisot substitutions
• Algorithm for determining pure pointedness of self-affine tilings
• The quality of the diophantine approximations found by the Jacobi--Perron algorithm and related algorithms
• Substitutions in dynamics, arithmetics and combinatorics
• Diffusion for chaotic plane sections of 3-periodic surfaces
• Fusion: a general framework for hierarchical tilings of \(\mathbb{R }^d\)
• Open problems in dynamics and related fields
• Weak mixing and eigenvalues for Arnoux-Rauzy sequences
• Substitution dynamical systems. Spectral analysis
• Coding of a translation of the two-dimensional torus
• Invariant measures for maps of continued fraction type
• Modified Jacobi-Perron algorithm and generating Markov partitions for special hyperbolic toral automorphisms
• Parallelogram tilings and Jacobi-Perron algorithm
• Balances for fixed points of primitive substitutions.
• Balance properties of multi-dimensional words
• Discrete planes, \({\mathbb Z}^2\)-actions, Jacobi-Perron algorithm and substitutions
• Symbolic discrepancy and self-similar dynamics.
• Self-affine tiling via substitution dynamical systems and Rauzy fractals.
• On simultaneous approximation to \((\alpha,\alpha^2)\) with \(\alpha^3+k\alpha-1=0\).
• Pure discrete spectrum in substitution tiling spaces
• Random product of substitutions with the same incidence matrix
• Sets of bounded discrepancy for multi-dimensional irrational rotation
• Atomic surfaces, tilings and coincidence. I: Irreducible case
• Prime flows in topological dynamics
• Bispecial Factors in the Brun S-Adic System
• A combinatorial approach to products of Pisot substitutions
• BALANCE PROPERTIES OF ARNOUX–RAUZY WORDS
• Generating Discrete Planes with Substitutions
• Balancedness of Arnoux-Rauzy and Brun Words
• Fusion tilings with infinite local complexity
• Substitutive Arnoux-Rauzy sequences have pure discrete spectrum
• On the Hausdorff dimension of the Rauzy gasket
• Valeurs propres des systèmes dynamiques définis par des substitutions de longueur variable
• Topological properties of Rauzy fractals
• Finite beta-expansions
• Extensions of Jentzsch's Theorem
• Some Monoids of Pisot Matrices
• Geometric theory of unimodular Pisot substitutions
• Best simultaneous diophantine approximations of Pisot numbers and Rauzy fractals
• Sturmian and Episturmian Words
• NONSTATIONARY MIXING AND THE UNIQUE ERGODICITY OF ADIC TRANSFORMATIONS
• Nombres algébriques et substitutions
• Substitutional dynamical systems, Bratteli diagrams and dimension groups
• A simple proof of the exponential convergence of the modified Jacobi–Perron algorithm
• Représentation géométrique de suites de complexité $2n+1$
• The spectrum of dynamical systems arising from substitutions of constant length
• Mesures de Gauss pour des algorithmes de fractions continues multidimensionnelles
• Dynamics of self-similar tilings
• When size matters: subshifts and their related tiling spaces
• Linearly recurrent subshifts have a finite number of non-periodic subshift factors
• A generalization of Sturmian sequences: Combinatorial structure and transcendence
• The Pisot conjecture for -substitutions
• Diffusion for the periodic wind-tree model
• Beyond substitutive dynamical systems: S-adic expansions
• Recognizability for sequences of morphisms
• On almost everywhere exponential convergence of the modified Jacobi-Perron algorithm: a corrected proof
• On the Pisot Substitution Conjecture
• Substitutions, Rauzy fractals and tilings
• Anosov families, renormalization and non-stationary subshifts
• MULTIDIMENSIONAL STURMIAN SEQUENCES AND GENERALIZED SUBSTITUTIONS
• Stationary Processes and Prediction Theory. (AM-44)
• Pisot substitutions and Rauzy fractals
• The scenery flow for geometric structures on the torus: The linear setting
• Bounded remainder sets
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