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Comptes Rendus. Mathématique
Combinatorics, Dynamical systems
A Rauzy fractal unbounded in all directions of the plane
Comptes Rendus. Mathématique, Volume 359 (2021) no. 4, pp. 399-407.

We construct an Arnoux–Rauzy word for which the set of all differences of two abelianized factors is equal to 3 . In particular, the imbalance of this word is infinite – and its Rauzy fractal is unbounded in all directions of the plane.

Nous construisons explicitement un mot d’Arnoux–Rauzy pour lequel l’ensemble des différences possibles des facteurs abélianisés est égal à 3 . En particulier, le déséquilibre de ce mot est infini, et son fractal de Rauzy n’est borné dans aucune direction du plan.

Received:
Revised:
Accepted:
Published online:
DOI: https://doi.org/10.5802/crmath.162
Mélodie Andrieu 1

1. Institut de Mathématiques de Marseille, I2M, Marseille, France
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Mélodie Andrieu. A Rauzy fractal unbounded in all directions of the plane. Comptes Rendus. Mathématique, Volume 359 (2021) no. 4, pp. 399-407. doi : 10.5802/crmath.162. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.162/

[1] Mélodie Andrieu Exceptional trajectories in the symbolic dynamics of multidimentional continued fraction algorithms (2021) (Ph. D. Thesis)

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