On the connection of the Riemann problem with properties of a dynamical system

We give the construction of an operator acting in a Hilbert space such that the Riemann hypothesis on zeros of the zeta-function is equivalent to the problem of the existence of an eigenvector for this operator with eigenvalue $-1$. We give also the construction of a dynamical system which turns out to be related to the Riemann hypothesis in the following way: for each complex zero of the zeta-function not lying on the critical line, there is a periodical trajectory of order two having a special form.