no. 4
Combinatoire, Systèmes dynamiques
A Rauzy fractal unbounded in all directions of the plane
Andrieu, Mélodie1
1 Institut de Mathématiques de Marseille, I2M, Marseille, France
Comptes Rendus. Mathématique, Tome 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 ℤ 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 ℤ 3 . En particulier, le déséquilibre de ce mot est infini, et son fractal de Rauzy n’est borné dans aucune direction du plan.

Reçu le :
Révisé le :
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DOI : 10.5802/crmath.162

Andrieu, Mélodie 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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Andrieu, Mélodie. A Rauzy fractal unbounded in all directions of the plane. Comptes Rendus. Mathématique, Tome 359 (2021) no. 4, pp. 399-407. doi: 10.5802/crmath.162

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