Comptes Rendus
Dynamical Systems
Geometry of the common dynamics of Pisot substitutions with the same incidence matrix
[Géométrie commune des substitutions Pisot de même matrice d'incidence]
Comptes Rendus. Mathématique, Volume 348 (2010) no. 17-18, pp. 1005-1008.

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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DOI : 10.1016/j.crma.2010.07.030

Tarek Sellami 1, 2

1 Institut de mathématiques de Luminy, CNRS U.M.R. 6206, 163, avenue de Luminy, case 907, 13288 Marseille cedex 09, France
2 Département de mathématiques, faculté des sciences de Sfax, BP 802, 3018 Sfax, Tunisia
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Tarek Sellami. Geometry of the common dynamics of Pisot substitutions with the same incidence matrix. Comptes Rendus. Mathématique, Volume 348 (2010) no. 17-18, pp. 1005-1008. doi : 10.1016/j.crma.2010.07.030. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.07.030/

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