ON FINITE CHARACTER GEOMETRICAL PROPERTY OF THE DIFFERENTIAL REALIZATION OF NONSTATIONARY HYPERBOLIC SYSTEMS

Topological-algebraic investigation of the problem of existence of realization of finite-dimensional continuous dynamic processes in the class of second-order ordinary differential equations in a separable Hilbert space has been conducted. Simultaneously, analyticalgeometric conditions of continuity of the process of constructing projections for the Rayleigh -Ritz nonlinear functional operator together with computation of the fundamental group of its image have been determined. The results may be applied to a posteriori modeling nonstationary hyperbolic systems.