On quantum quadratic operators of 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 M 2 ( 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.