[Géométrie commune des substitutions Pisot de même matrice d'incidence]
À toute substitution Pisot, on sait associer, par projection de la ligne brisée associée à un point fixe infini de la substitution, un ensemble borné aux propriétés intéressantes, appelé fractal de Rauzy. Deux substitutions ayant la même matrice d'incidence peuvent avoir des fractals de Rauzy très différents. Nous montrons que, sous des conditions faibles, l'intersection de ces deux fractals est de mesure non nulle, et peut aussi être engendrée par une substitution.
Any Pisot substitution can be associated with a bounded set with interesting properties, called the Rauzy fractal. This set is obtained by projection of the broken line associated with an infinite fixed point. Two substitutions having the same incidence matrix can have different Rauzy fractals. We show that under weak conditions, the intersection of these two fractals has strictly positive measure, and can also be generated by a substitution.
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@article{CRMATH_2010__348_17-18_1005_0,
author = {Sellami, Tarek},
title = {Geometry of the common dynamics of {Pisot} substitutions with the same incidence matrix},
journal = {Comptes Rendus. Math\'ematique},
pages = {1005--1008},
publisher = {Elsevier},
volume = {348},
number = {17-18},
year = {2010},
doi = {10.1016/j.crma.2010.07.030},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2010.07.030/}
}
TY - JOUR AU - Sellami, Tarek TI - Geometry of the common dynamics of Pisot substitutions with the same incidence matrix JO - Comptes Rendus. Mathématique PY - 2010 SP - 1005 EP - 1008 VL - 348 IS - 17-18 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2010.07.030/ DO - 10.1016/j.crma.2010.07.030 LA - en ID - CRMATH_2010__348_17-18_1005_0 ER -
%0 Journal Article %A Sellami, Tarek %T Geometry of the common dynamics of Pisot substitutions with the same incidence matrix %J Comptes Rendus. Mathématique %D 2010 %P 1005-1008 %V 348 %N 17-18 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2010.07.030/ %R 10.1016/j.crma.2010.07.030 %G en %F CRMATH_2010__348_17-18_1005_0
Sellami, Tarek. Geometry of the common dynamics of Pisot substitutions with the same incidence matrix. Comptes Rendus. Mathématique, Tome 348 (2010) no. 17-18, pp. 1005-1008. doi : 10.1016/j.crma.2010.07.030. http://www.numdam.org/articles/10.1016/j.crma.2010.07.030/
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