Nous construisons explicitement un mot d’Arnoux–Rauzy pour lequel l’ensemble des différences possibles des facteurs abélianisés est égal à . 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 . 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
@article{CRMATH_2021__359_4_399_0, author = {Andrieu, M\'elodie}, title = {A {Rauzy} fractal unbounded in all directions of the plane}, journal = {Comptes Rendus. Math\'ematique}, pages = {399--407}, publisher = {Acad\'emie des sciences, Paris}, volume = {359}, number = {4}, year = {2021}, doi = {10.5802/crmath.162}, mrnumber = {4264322}, zbl = {07362160}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/crmath.162/} }
TY - JOUR AU - Andrieu, Mélodie TI - A Rauzy fractal unbounded in all directions of the plane JO - Comptes Rendus. Mathématique PY - 2021 SP - 399 EP - 407 VL - 359 IS - 4 PB - Académie des sciences, Paris UR - http://archive.numdam.org/articles/10.5802/crmath.162/ DO - 10.5802/crmath.162 LA - en ID - CRMATH_2021__359_4_399_0 ER -
%0 Journal Article %A Andrieu, Mélodie %T A Rauzy fractal unbounded in all directions of the plane %J Comptes Rendus. Mathématique %D 2021 %P 399-407 %V 359 %N 4 %I Académie des sciences, Paris %U http://archive.numdam.org/articles/10.5802/crmath.162/ %R 10.5802/crmath.162 %G en %F CRMATH_2021__359_4_399_0
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. http://archive.numdam.org/articles/10.5802/crmath.162/
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