Outputs (2)

Aperiodicity, rotational tiling spaces and topological space groups (2021)
Journal Article
Hunton, J., & Walton, J. (2021). Aperiodicity, rotational tiling spaces and topological space groups. Advances in Mathematics, 388, Article 107855. https://doi.org/10.1016/j.aim.2021.107855

We study the rotational structures of aperiodic tilings in Euclidean space of arbitrary dimension using topological methods. Classical topological approaches to the study of aperiodic patterns have largely concentrated just on translational structure... Read More about Aperiodicity, rotational tiling spaces and topological space groups.

Chaotic Delone Sets (2021)
Journal Article
Alvarez Lopez, J. A., Barral Lijo, R., Hunton, J., Nozawa, H., & Parker, J. R. (2021). Chaotic Delone Sets. Discrete and Continuous Dynamical Systems - Series A, 41(8), 3781-3796. https://doi.org/10.3934/dcds.2021016

We present a definition of chaotic Delone set and establish the genericity of chaos in the space of (ϵ,δ)-Delone sets for ϵ≥δ. We also present a hyperbolic analogue of the cut-and-project method that naturally produces examples of chaotic Delone sets... Read More about Chaotic Delone Sets.