Seminarium KMMF "Teoria Dwoistości"

In the first part of the talk I will give tendentious introduction todiscrete integrable systems. In the second part of the talkI will present two lists of two-component systems of integrable difference equations defined on the edges of the $\mathbb{Z}^2$ graph. The systems of difference equations give us in turn quadrirational Yang-Baxter maps. The integrability of these systems is manifested by their Lax formulation which is a consequence of the multi-dimensional compatibility of these systems. Imposing constraints consistent with the systems of difference equations, I recover known integrable quad-equations including the discrete version of the Krichever-Novikov equation.