George S. Osipenko
National technical university, Sebastopol, Ukraine
A V. Krupin
National technical university, Sebastopol, Ukraine
A. A. Bezruchko
National technical university, Sebastopol, Ukraine
Eugene I. Petrenko
Russia, 198904, Saint Petersburg, Petrodvorets, Universitetskiy pr. 4
Saint Petersburg State University
Faculty of mathematics and mechanics
A. Ya. Kapitanov
Saint Petersburg State Technical University, Russia
Let f from M to M be a homeomorphism of a compact manifold M, where M is subset of Rd generating the discrete dynamical system { fn, n from Z}. The based on the concept of symbolic image algorithm for the construction of an invariant measure is proposed. A sequence of subdivisions with maximal diameters dk tends to 0 and the corresponding sequence Gk of symbolic images are considered. On the images the matched invariant flows mk are constructed. The compositions of the flows and a Lebesgue measure are used to define the measures mk. Given the conditions it is proved that there exists an f-invariant measure m such that m is the limit of mk as on dk approaches 0 in weak topology.