Numeration systems and Markov partitions from self similar tilings

DOI10.1090/S0002-9947-99-02360-0zbMath0984.11008OpenAlexW1554576426MaRDI QIDQ4243647

Brenda Praggastis

Publication date: 19 May 1999

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

Full work available at URL: https://doi.org/10.1090/s0002-9947-99-02360-0

zbMATH Keywords

Markov partitionsdigit expansionshyperbolic toral automorphismsfractal self-similar tilings

Mathematics Subject Classification ID

Related Items (39)

Dynamical directions in numeration ⋮ Fractal representation of the attractive lamination of an automorphism of the free group. ⋮ Atomic surfaces, tilings and coincidences. II: Reducible case ⋮ Periodicity ofβ-expansions for certain Pisot units ⋮ On purely periodic beta-expansions of Pisot numbers ⋮ On the characterization of expansion maps for self-affine tilings ⋮ A survey on topological properties of tiles related to number systems ⋮ Second-order ergodic theorem for self-similar tiling systems ⋮ Decidability Problems for Self-induced Systems Generated by a Substitution ⋮ On arithmetic progressions in non-periodic self-affine tilings ⋮ On substitution tilings and Delone sets without finite local complexity ⋮ Algorithm for determining pure pointedness of self-affine tilings ⋮ Limit theorems for self-similar tilings ⋮ Proximality and pure point spectrum for tiling dynamical systems ⋮ Dual systems of algebraic iterated function systems ⋮ Introduction to Hierarchical Tiling Dynamical Systems ⋮ Beta-expansions, natural extensions and multiple tilings associated with Pisot units ⋮ Boundary of the Rauzy fractal sets in \(\mathbb {R} \times \mathbb {C}\) generated by \(P(x) = x^4 - x^3 - x^2 - x - 1\) ⋮ Purely periodic \(\beta \)-expansions in the Pisot non-unit case ⋮ Symbolic dynamics and Markov partitions ⋮ Tilings Described by Iterated Maps ⋮ Symbolic Representations and ${\mathbb T}^n$ Automorphisms ⋮ Tilings for Pisot beta numeration ⋮ Atomic surfaces, tilings and coincidence. I: Irreducible case ⋮ Pure point diffractive substitution Delone sets have the Meyer property ⋮ Purely periodic points of complex Pisot expansions ⋮ Periodic codings of algebraic graph-directed IFS ⋮ A Markov partition that reflects the geometry of a hyperbolic toral automorphism ⋮ On a class of Rauzy fractals without the finiteness property ⋮ Topology of planar self-affine tiles with collinear digit set ⋮ Topological properties of a class of cubic Rauzy fractals ⋮ \(AH\)-substitution and Markov partition of a group automorphism on \(T^d\) ⋮ Substitutive number systems ⋮ Boundary of central tiles associated with Pisot beta-numeration and purely periodic expansions ⋮ A combinatorial approach to products of Pisot substitutions ⋮ Markov partitions for toral \(\mathbb{Z}^2\)-rotations featuring Jeandel-Rao Wang shift and model sets ⋮ Invariant measures for non-primitive tiling substitutions ⋮ A class of cubic Rauzy fractals ⋮ Numeration systems and Markov partitions from self similar tilings

Cites Work

• Unnamed Item
• Unnamed Item
• Inflationary tilings with a similarity structure
• Finite beta-expansions
• Markov Partitions are not Smooth
• On theβ-expansions of real numbers
• Nombres algébriques et substitutions
• The Fractal Dimension of Sets Derived from Complex Bases
• Smooth Markov partitions and toral automorphisms
• Topological entropy and equivalence of dynamical systems
• Numeration systems and Markov partitions from self similar tilings
• Dynamical properties of quasihyperbolic toral automorphisms
• An Introduction to Symbolic Dynamics and Coding
• Similarity of automorphisms of the torus
• Markov Partitions for Axiom A Diffeomorphisms

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