George Osipenko
Saint-Petersburg State Technical University,
29 Politehnicheskaja str., 195251 St.Petersburg, RUSSIA,
Laboratory of Nonlinear Analysis
In the paper we present a new constructive method for the study of global structure of dynamical system. A dynamical system is associated with an oriented graph called a symbolic image of the system. The symbolic image can be considered as a finite approximation of a dynamical system. An investigation of the symbolic image gives an opportunity to obtain a neighborhood of the set of chain recurrent trajectories. An algorithm for localization of the chain recurrent set is suggested. A periodic shadowing theorem is established.