Beta-expansions, natural extensions and multiple tilings associated with Pisot units

DOI10.1090/S0002-9947-2012-05362-1zbMath1295.11010arXiv0907.2676OpenAlexW3105233392MaRDI QIDQ5390239

Wolfgang Steiner, Charlene Kalle

Publication date: 27 April 2012

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

Full work available at URL: https://arxiv.org/abs/0907.2676

zbMATH Keywords

natural extensionbeta-expansionmultiple tilingPisot unit

Mathematics Subject Classification ID

Measure-preserving transformations (28D05) Fractals (28A80) Symbolic dynamics (37B10) PV-numbers and generalizations; other special algebraic numbers; Mahler measure (11R06) Quasicrystals and aperiodic tilings in discrete geometry (52C23) Other number representations (11A67)

Related Items (29)

On the structure of (−β)-integers ⋮ On periodic representations in non-Pisot bases ⋮ Fractal tiles associated with shift radix systems ⋮ Rational self-affine tiles ⋮ Fiber denseness of intermediate β-shifts of finite type ⋮ Natural extensions for piecewise affine maps via Hofbauer towers ⋮ Intermediate \(\beta\)-shifts as greedy \(\beta\)-shifts with a hole ⋮ Arithmetics in numeration systems with negative quadratic base ⋮ Matching for a family of infinite measure continued fraction transformations ⋮ Numbers with integer expansion in the numeration system with negative base ⋮ Bifurcations of digit frequencies in unique expansions ⋮ On universal and periodic \(\beta\)-expansions, and the Hausdorff dimension of the set of all expansions ⋮ Greedy and lazy representations in negative base systems ⋮ Dual systems of algebraic iterated function systems ⋮ Number representation using generalized \((-\beta )\)-transformation ⋮ Representations for complex numbers with integer digits ⋮ Denseness of intermediate $\beta $-shifts of finite-type ⋮ The geometry of non-unit Pisot substitutions ⋮ Multiple tilings associated to \(d\)-Bonacci beta-expansions ⋮ The Pisot conjecture for -substitutions ⋮ Matching for generalised \(\beta\)-transformations ⋮ Tilings for Pisot beta numeration ⋮ Periodic codings of algebraic graph-directed IFS ⋮ Expansions in multiple bases ⋮ Dynamical properties of the tent map ⋮ Intermediate \(\beta\)-shifts of finite type ⋮ Substitutive number systems ⋮ Critical itineraries of maps with constant slope and one discontinuity ⋮ On the specification property and synchronization of uniqueq-expansions

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