Algebraic numbers, free group automorphisms and substitutions on the plane

DOI10.1090/S0002-9947-2011-05188-3zbMath1254.37015OpenAlexW2050250729MaRDI QIDQ3092812

Edmund Harriss, Pierre Arnoux, Shunji Ito, Maki Furukado

Publication date: 11 October 2011

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-2011-05188-3

zbMATH Keywords

non-Pisot substitutionsubstitution rules for tiling

Mathematics Subject Classification ID

Related Items (16)

Representations of toral automorphisms ⋮ Topologically mixing tiling of generated by a generalized substitution ⋮ Decidability Problems for Self-induced Systems Generated by a Substitution ⋮ Combinatorial generation of planar sets ⋮ Approximation of digital surfaces by a hierarchical set of planar patches ⋮ Algorithm for determining pure pointedness of self-affine tilings ⋮ Brun expansions of stepped surfaces ⋮ Substitution discrete plane tilings with \(2n\)-fold rotational symmetry for odd \(n\) ⋮ Stepped surfaces and Rauzy fractals induced from automorphisms on the free group of rank 2 ⋮ Representations for complex numbers with integer digits ⋮ Introduction to Hierarchical Tiling Dynamical Systems ⋮ S-adic Sequences: A Bridge Between Dynamics, Arithmetic, and Geometry ⋮ Geometrical models for a class of reducible Pisot substitutions ⋮ Purely periodic points of complex Pisot expansions ⋮ \(AH\)-substitution and Markov partition of a group automorphism on \(T^d\) ⋮ Markov partitions for toral \(\mathbb{Z}^2\)-rotations featuring Jeandel-Rao Wang shift and model sets

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Canonical substitutions tilings of Ammann-Beenker type
• Substitutions in dynamics, arithmetics and combinatorics
• Numeration systems, fractals and stochastic processes
• Tilings from non-Pisot unimodular matrices
• Train tracks and automorphisms of free groups
• Some properties of invertible substitutions of rank \(d\), and higher dimensional substitutions.
• Cohomology of canonical projection tilings
• The construction of self-similar tilings
• Tilings associated with non-Pisot matrices
• One-dimensional non-wandering sets
• A Markov partition that reflects the geometry of a hyperbolic toral automorphism
• Markov Partitions are not Smooth
• Geometric theory of unimodular Pisot substitutions
• Nombres algébriques et substitutions
• The dynamical properties of Penrose tilings
• Arithmetic construction of sofic partitions of hyperbolic toral automorphisms
• Similarity of automorphisms of the torus
• The undecidability of the domino problem
• Markov Partitions for Axiom A Diffeomorphisms
• Expanding attractors
• Higher dimensional extensions of substitutions and their dual maps
• Pisot substitutions and Rauzy fractals
• Characterization of planar pseudo-self-similar tilings

This page was built for publication: Algebraic numbers, free group automorphisms and substitutions on the plane