  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
Tychonoff topology as the diameter of the covering tends to zero. For a cycle
on G going through different vertices, a simple flow is by definition a uniform
distribution on arcs of this cycle. We show that simple flows converge to
ergodic measures in the weak topology as the diameter of the covering tends to
zero.
