Chaotic Delone sets

TL;DR

This paper introduces the concept of chaotic Delone sets, proves that chaos is generic among certain Delone sets, and provides a hyperbolic cut-and-project method to generate examples of such chaotic sets.

Contribution

It defines chaotic Delone sets, demonstrates their genericity, and develops a hyperbolic analogue of the cut-and-project method for constructing these sets.

Findings

Chaos is generic in the space of $(psilon,elta)$-Delone sets for psilon elta

A hyperbolic cut-and-project method produces examples of chaotic Delone sets

The paper establishes a new framework linking chaos and 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 $\epsilon\geq \delta$. We also present a hyperbolic analogue of the cut-and-project method that naturally produces examples of chaotic Delone sets.