Chaotic Delone sets

Abstract

We present a definition of chaotic Delone set, and establish the genericity of chaos in the space of $(\epsilon ,\delta )$-Delone sets for $\epsilon \ge \delta$. We also present a hyperbolic analogue of the cut-and-project method that naturally produces examples of chaotic Delone sets.

16 pages, 6 figures. Corrections to previous version: miscellanous editorial changes, we have added section 5 where we explain how to obtain chaotic Delone sets on R^n by taking products. To appear on Discrete and Continuous Dynamical Systems A