On the representation of Riemann zeta-function in the critical strip over an infinite product of second-order matrics and on a dynamical system

The representations of Riemann zeta-function over an infinite products of second-order matrics converging in the critical strip are obtained. This result allows to construct a dynamical system is connected with Riemann problem on zeros of the zeta-function so that a second-order periodic trajectory of a special type corresponds to every complex zero not situated on the critical line. A certain operator acting in a Hilbert space, which has an eigenvector with eigenvalue $(-1)$ if an only if Riemann zeta-function has a complex zero not situated on the critical line, is used in the construction of a dynamical system.