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

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.

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.

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DOI : 10.5802/crmath.162

Mélodie Andrieu 1

1 Institut de Mathématiques de Marseille, I2M, Marseille, France
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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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/

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