Model sets with positive entropy in Euclidean cut and project schemes
[Ensembles modèles à entropie positive dans des schémas par coupe et projection]
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 52 (2019) no. 5, pp. 1073-1106.
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On construit des ensembles de Delone euclidiens obtenus par coupe et projection de sorte que l'entropie des systèmes dynamiques associés soit strictement positive. La construction permet d'utiliser une fenêtre propre ou d'intérieur vide. Dans une construction probabiliste, pour presque tout paramètre, l'entropie est proportionnelle à la mesure de la frontière de la fenêtre.

We construct model sets arising from cut and project schemes in Euclidean spaces whose associated Delone dynamical systems have positive topological entropy. The construction works both with windows that are proper and with windows that have empty interior. In a probabilistic construction with randomly generated windows, the entropy almost surely turns out to be proportional to the measure of the boundary of the window.

DOI : 10.24033/asens.2403
Classification : 52C23; 37B50, 37B10 
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     title = {Model sets with positive entropy in {Euclidean} cut and project schemes},
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     pages = {1073--1106},
     publisher = {Soci\'et\'e Math\'ematique de France. Tous droits r\'eserv\'es},
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Jäger, Tobias; Lenz, Daniel; Oertel, Christian. Model sets with positive entropy in Euclidean cut and project schemes. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 52 (2019) no. 5, pp. 1073-1106. doi : 10.24033/asens.2403. http://www.numdam.org/articles/10.24033/asens.2403/

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