Pure discrete spectrum dynamical system and periodic tiling associated with a substitution

DOI10.5802/aif.2021zbMath1083.37009OpenAlexW2329881353MaRDI QIDQ1890159

Anne Siegel

Publication date: 20 December 2004

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

Full work available at URL: http://www.numdam.org/item?id=AIF_2004__54_2_341_0

zbMATH Keywords

tilingsRauzy fractalsubstitutionpure discrete spectrum

Mathematics Subject Classification ID

Ergodic theory of linear operators (47A35) Fractals (28A80) Symbolic dynamics (37B10) Tilings in (n) dimensions (aspects of discrete geometry) (52C22)

Related Items

Symmetric and congruent Rauzy fractals ⋮ 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 ⋮ Substitutions, abstract number systems and the space filling property ⋮ A connection between palindromic and factor complexity using return words ⋮ Episturmian words: a survey ⋮ Unimodular Pisot substitutions and their associated tiles ⋮ Algorithm for determining pure pointedness of self-affine tilings ⋮ Conjugacy of unimodular Pisot substitution subshifts to domain exchanges ⋮ Dual systems of algebraic iterated function systems ⋮ Beta-expansions, natural extensions and multiple tilings associated with Pisot units ⋮ Atomic surfaces, tilings and coincidence. I: Irreducible case ⋮ Non-Unimodularity ⋮ Geometry of the common dynamics of flipped Pisot substitutions

Cites Work

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• Linearly recurrent subshifts have a finite number of non-periodic subshift factors
• Geodesic laminations as geometric realizations of Pisot substitutions
• Frontière du fractal de Rauzy et système de numération complexe
• Substitution dynamical systems : algebraic characterization of eigenvalues
• Pisot substitutions and Rauzy fractals

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