There is a family of birational self-mappings of the plane arising from the theory of cluster algebra mutations that was studied previously by Machacek-Ovenhouse from the perspective of real dynamics. We study this family of mappings from the perspective of complex dynamics and, in particular, show that is most cases there is no conserved quantity. No background on cluster algebras is expected from the audience.

This is the joint-work with Andrei Grigorev, Andres Quintero and Roland Roeder.