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 \(M(j)\) . The paths of the symbolic image correspond to the pseudo-trajectories of the system. By associating sequences of points in M with symbolic sequences, we can analyze the system’s behavior in a more tractable format.