ON COMPRESSIBILITY AREA OF UNSTABLE DIFFERENCE-DYNAMIC SYSTEMS AND DETERMINATED CHAOS - Bapaev, K.B.; Vassilina, G.K.; Slamzhanova, S.S. (Academic Scientific Journal of Computer Science, 2020)
In this paper saddle-point bifurcation is studied. It is shown that as a result of bifurcation or collision of stable and unstable points, they leave the area. In other words, they go into chaos, i.e. in a state of disorder. Here the normalization method is used to identify the bifurcation point. Unstable in the sense of Lyapunov differencedynamic systems are considered. In the first part of the paper, the transformation of linear systems in instability case is given. A linear system with a diagonal matrix is considered. It is shown that in a neighborhood of zero this system is not reduced to a special form with the help of non-degenerate transformations. It is proved that for non-degenerate transformations the trajectories of a system of a special form from a neighborhood of the origin cannot be displayed in the trajectory of solutions of a given linear system. Thus, the topology of the neighborhood of the zero point of a system of a special form does not transform into the topology of a given system in a neighborhood of zero. The causes of the contradiction obtained by applying this method are shown. In the second part, analytic difference-dynamical systems and analytic homeomorphisms are considered. Also compressive difference-dynamical systems are investigated. The concept of compressing difference-dynamical systems is given. It is shown to which system the  -compressing difference-dynamical systems are isomorphic.