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.

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DOI: 10.5802/crmath.162
Andrieu, Mélodie 1

1 Institut de Mathématiques de Marseille, I2M, Marseille, France
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Andrieu, Mélodie. 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. http://archive.numdam.org/articles/10.5802/crmath.162/

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