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

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On Application of Balance Method to Approximation of Invariant Measures of a Dynamical System


N. Ampilova

Russia, 198504, Petergof, Universitetski pr.28
Saint-Peterburg State University
Faculty of Mathematics and Mechanics

Eugene I. Petrenko

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


Invariant measures of a dynamical system describe the asymptotic behaviour of its orbits, hence the elaboration of numerical methods of their approximation is of considerable importance in applications. We use the concept of symbolic image which is a finite approximation of a dynamical system. Symbolic image is constructed as an oriented graph for a mapping f and a fixed covering of its phase space. Vertices of the graph correspond to the cells of the covering and edges mark the existence of nonempty intersections of the covering cells with their images. We construct an invariant measure (stationary process) on the graph of symbolic image, which is the approximation of an invariant measure of the initial system. Application of balance method allows us to construct an invariant measure in such a way to assign the measure to all edges of the graph.

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