On the Approximate Periodicity of Sequences Attached to Non-Crystallographic Root Systems

Lampe P. On the Approximate Periodicity of Sequences Attached to Non-Crystallographic Root Systems. EXPERIMENTAL MATHEMATICS. 2018;27(3):265-271.We study Fomin-Zelevinsky's mutation rule in the context of non-crystallographic root systems. In particular, we construct approximately periodic sequences of real numbers for the non-crystallographic root systems of rank 2 by adjusting the exchange relation for cluster algebras. Moreover, we describe matrix mutation classes for types H-3 and H-4