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

Several new mutation-periodic quivers of period higher than 1 are introduced as well as the associated discrete dynamical systems. The reduction of these systems is developed using either a presymplectic or a Poisson approach. The presymplectic approach leads to a reduced system whose iteration map is symplectic with respect to a log symplectic form. In the Poisson approach we build a Poisson structure invariant under the iteration map, leading to a reduced system whose variables are the Casimirs of such structure.