On quantum quadratic operators of M2(C) and their dynamics

In the present paper we study nonlinear dynamics of quantum quadratic operators (q.q.o.) acting on the algebra of 2×2 matrices M2(C). First, we describe q.q.o. with Haar state as well as quadratic operators with the Kadison-Schwarz property. By means of such a description we provide an example of q.q.o. which is not the Kadison-Schwarz operator. Then we study stability of dynamics of q.q.o.