We consider a discrete dynamical system on a compact manifold M generated by a homeomorphism f. Let \(C = \{M(i)\}\) be a finite covering of M by closed cells. The symbolic image of a dynamical system is a directed graph G with vertices corresponding to cells in which vertices i and j are joined by an arc \(i \to j\) if the image \(f(M(i))\) intersects \(M(j)\) . We show that the set of paths of the symbolic image converges to the set of trajectories of the system in the Tikhonov topology as the diameter of the covering tends to zero. A method for identifying a chain-recurrent set is introduced. As an illustration, we examine the localization of the chaotic set within the Ikeda dynamic system.