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Abstract

This paper is a study of the global structure of the attractors of a dynamical system. The dynamical system is associated with an oriented graph called a Symbolic Image of the system. The symbolic image can be considered as a finite discrete approximation of the dynamical system flow. Investigation of the symbolic image provides an opportunity to localize the attractors of the system and to estimate their domains of attraction. A special sequence of symbolic images is considered in order to obtain precise knowledge about the global structure of the attractors and to get filtrations of the system.