To a posteriori modeling nonstationary hyperbolic systems

In the context of the qualitative theory of differential implementation of infinite-dimensional controlled dynamical systems contains the results of research topology-algebraic properties of families of continuous dynamic processes (mappings, “input-output”) to the problem of solvability of the realization of these families in the class of nonstationary ordinary differential equations of the second order (including hyperbolic) in a separable Hilbert space. Along the way, substan-extracting analytic-geometric continuity conditions of projectivization nonlinear operator Rayleigh-Ritz calculation of the fundamental group of its image.