Reduction of cluster iteration maps to symplectic maps

Abstract

We study iteration maps of recurrence relations arising from mutation periodic quivers of arbitrary period. Combining tools from cluster algebra theory and (pre)symplectic geometry, we show that these cluster iteration maps can be reduced to symplectic maps on a lower dimensional submanifold, provided the matrix representing the quiver is singular. The reduced iteration map is explicitly computed for several new periodic quivers.

17 pages

Cited by in corpus (1)

• Discrete dynamical systems from mutation-periodic quivers: examples and reduction