Dynamic chaos

The main moments of the historical development of one of the basic methods of nonlinear systems investigating (the averaging method) are traced. This method is understood as a transition from the so-called exact equation:

In the paper we studied properties of conservative singular maps. It was found that under some conditions the intermittency without chaotic phases can be observed in these maps. The alternative mechanism of the intermittency origin in Hamiltonian singular systems was considered. Its general properties were discussed. We studied special properties of phase space structure in these systems. It is shown that Hamiltonian intermittency can be characterized by zero Lyapunov exponents. It gives us the possibility to classify it as pseoudochaos dynamics.

Dynamic chaos – a remarkable milestone development of science of the last centuryhas attracted the attention of different areas of knowledge. Chaos theory describes not only a wide range of phenomena in various fields of physics and other natural sciences and penetrates into the humanitarian sphere, but also significantly influenced the scientific picture of the world. What features of the development of science, economic and social conditions led to that long and difficult path of discovery of chaos began precisely at the end of the XIX century and stretched out for decades?