By T.G. Vozmischeva
Introd uction the matter of integrability or nonintegrability of dynamical structures is likely one of the vital difficulties of arithmetic and mechanics. Integrable instances are of substantial curiosity, seeing that, through studying them, it is easy to research common legislation of habit for the strategies of those structures. The classical method of learning dynamical structures assumes a look for particular formulation for the ideas of movement equations after which their research. This strategy motivated the improvement of latest parts in arithmetic, resembling the al gebraic integration and the idea of elliptic and theta capabilities. having said that, the qualitative tools of learning dynamical structures are a lot genuine. It was once Poincare who based the qualitative idea of differential equa tions. Poincare, figuring out qualitative tools, studied the issues of celestial mechanics and cosmology during which it truly is particularly very important to appreciate the habit of trajectories of movement, i.e., the options of differential equations at countless time. particularly, starting from Poincare structures of equations (in reference to the examine of the issues of ce lestial mechanics), the right-hand components of which do not rely explicitly at the autonomous variable of time, i.e., dynamical structures, are studied.
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