Model sets with positive entropy in Euclidean cut and project schemes

Abstract

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

Revised version with a number of corrections and improvements. Most importantly, the constructions have been extended from one-dimensional examples to higher-dimensional ones. To appear in Ann. Sci. École Norm. Sup