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.