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.

Mathematical problems and theory of numerical methods