Arithmetic and dynamical properties of the Rauzy fractal
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Publication:1273185
DOI10.5802/jtnb.223zbMath0918.11048OpenAlexW2075708776MaRDI QIDQ1273185
Publication date: 17 March 1999
Published in: Journal de Théorie des Nombres de Bordeaux (Search for Journal in Brave)
Full work available at URL: http://www.numdam.org/item?id=JTNB_1998__10_1_135_0
Topological dynamics (37B99) Metric theory of other algorithms and expansions; measure and Hausdorff dimension (11K55) Fractals (28A80)
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Cites Work
- Unnamed Item
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- A sufficient condition for weak mixing of subtitutions and stationary adic transformations
- On Rauzy fractal
- Substitution dynamical systems - spectral analysis
- Systèmes de numération et fonctions fractales relatifs aux substitutions. (Numeration systems and fractal functions related to substitutions)
- Fractal geometry derived from complex bases
- Recurrent sets
- Digital sum problems and substitutions on a finite alphabet
- Arithmetic and dynamical properties of the Rauzy fractal
- On some dynamical subsets of the Rauzy fractal
- \(\beta\)-shift, numeration systems, and automata
- \(\alpha\)-expansions, linear recurrences, and the sum-of-digits function
- Valeurs propres des systèmes dynamiques définis par des substitutions de longueur variable
- Finite beta-expansions
- Nombres algébriques et substitutions
- The Fractal Dimension of Sets Derived from Complex Bases
- Systems of Numeration
- Développement en base $\theta$, répartition modulo un de la suite $(x\theta \sp n)$, n$\ge 0$, langages codés et $\theta$-shift
- Complex Numbers with Three Radix Expansions
- Représentation géométrique de suites de complexité $2n+1$
- Frontière du fractal de Rauzy et système de numération complexe
- Reconnaissabilité des substitutions et complexité des suites automatiques
- Odometers and systems of numeration
