On quantum quadratic operators of $\bm_2(\mathbb{C})$ and their dynamics

In the present paper we study nonlinear dynamics of quantum quadratic operators (q.q.o) acting on the algebra of $2\times 2$ matrices $\bm_2(\bc)$. 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 Kadision-Schwarz operator. Then we study stability of dynamics of q.q.o.

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