Abstract
Wide application of dynamical systems resulted in designing many various methods for investigations, both analytical and computer-oriented ones. In this paper we consider methods based on ideas of symbolic dynamics, and discuss the application of dynamical systems for solving identification and prognosis problems. The representation of the system dynamics by an oriented graph constructed in accordance with the system and a finite partition of the phase space gives a possibility to matchtrajectories paths on the graph. By this method one may construct approximation to invariant sets and invariant measures, and the Morse spectrum as well. Using dynamical systems in identification problems is consideredon examples of probability chainsfor the modeling social and economic resource distribution, and the method of nonlinear dynamics for reconstruction of an attractor on a given time series.
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