Reduction of order of cluster-type recurrence relations
Inês Cruz, M. Esmeralda Sousa-Dias
São Paulo Journal of Mathematical Sciences, 6 (2012), no. 2, 203-225.
Certain nonlinear recurrence relations (of the real line) can be studied within the framework of cluster algebra theory. For this type of relations we develop the tools of Poisson and pre-symplectic structures compatible with a cluster algebra, in order to understand how these structures enable to reduce the recurrence relation to one of lower order. Several examples are worked in detail.