Chaotic Delone sets

This article has been published in a revised form in Discrete and Continuous Dynamical Systems [http://dx.doi.org/10.3934/dcds.2021016]. This version is free to download for private research and study only. Not for redistribution, re-sale or use in derivative works.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 analog of the cut-and-project method that naturally produces examples of chaotic Delone sets.FEDER/Ministerio de Ciencia, Innovación y Universidades/AEI/MTM2017-89686-P [A.L., B.L., H.N.]; Xunta de Galicia/ED431C 2019/10 [A.L., B.L., H.N.]; JSPS Grant-in-Aid for Scientific Research 17K14195 [H.N]; Canon Foundation in Europe Research Fellowship [B.L].S