DYNAMICAL-SYSTEMS FROM QUANTUM INTEGRABILITY

We describe a class of non-linear transformations acting on many varia bles. These transformations have their origin in the theory of quantum integrability: they appear in the description of the symmetries of th e Yang-Baxter equations and their higher dimensional generalizations. They are generated by involutions and act as birational mappings on va rious projective spaces. We present numerous figures, showing successi ve iterations of these mappings. The existence of algebraic invariants explains the aspect of these figures. We also study deformations of o ur transformations.