ИСТИНА

The aim of the talk is to analyze the connection between Lyapunov exponents and invariant measures in projective bundle by using the symbolic image technique. Symbolic image of a dynamical system with respect to a covering is a directed graph with vertices corresponding to cells of the covering and edges corresponding to transitions between cells by system dynamics. The transformation of the system flow into a symbolic image allows reducing the problems of dynamical systems to the tasks on graphs. In this case a flow on the graph corresponds to an invariant measure and a mean of the graph labeling corresponds to a Lyapunov exponent. Symbolic image is a tool which may be successfully applied both to prove important results and to perform computer modelling of complex dynamical systems. The Morse spectrum is a collection of exponents of all orbits. The implementation of symbolic image gives an opportunity to calculate the Morse spectrum and to check hyperbolicity in complicated cases. The example of such a verification is given