On the approximate periodicity of sequences attached to   noncrystallographic root systems
  We study Fomin-Zelevinsky's mutation rule in the context of noncrystallographic root systems. In particular, we construct approximately periodic sequences of real numbers for the noncrystallographic root systems of rank 2 by adjusting the exchange relation for cluster algebras. Moreover, we describe matrix mutation classes for type H3 and H4. 
Philipp Lampe
math.DS math.RT