ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

Development and Implementation of Algorithms for Construction of the Symbolic Image


Eugene I. Petrenko

Russia, 198904, Saint Petersburg, Petrodvorets, Universitetskiy pr. 4
Saint Petersburg State University
Faculty of mathematics and mechanics


The intensive development of the theory of dynamical systems lead to the elaboration of many algorithms, and the growing power of computers resulted in that the methods of computer modeling are widely adopted.
To investigate dynamical systems we use the concept of symbolic image introduced by G.Osipenko. Given a homeomorphism f, phase space D and a finite covering Di the oriented graph G is constructed, being its nodes correspond to the cells of the covering and there is the edge i->j iff f(Di) intersects Dj.
The research of many problems for the initial system may be reduced to the symbolic image studying.
The article is devoted to the methods of construction of symbolic image. Several algorithms to construct the cell image are described. The results of their tests and comparison of performance are given.

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