ИСТИНА

Let f : M --> M be a diffeomorphism of a compact manifold M. Consider a smooth discrete system x_{n+1} = f(x_n) generated by the diffeomorphism f. Consider a nite closed covering C = {M(1); ....;M(n)} of M. The set M(i) is called a cell of index i. Let G be the directed graph with the vertices {i} corresponding to the cells {M(i)}. Vertices i and j are connected by a directed edge i --> j if and only if f(M(i))∩M(j) ̸= ∅. The graph G is called the symbolic image of the mapping f for the covering C. The investigation of the symbolic image enables one to obtain a useful information concerning the global structure of the dynamical system. On the example of checking the structural stability of the system, we show how the methods of symbolic analysis work.