By T.G. Vozmischeva

Introd uction the matter of integrability or nonintegrability of dynamical platforms is likely one of the significant difficulties of arithmetic and mechanics. Integrable situations are of substantial curiosity, seeing that, by way of reading them, you can examine normal legislation of habit for the ideas of those structures. The classical method of learning dynamical structures assumes a look for particular formulation for the strategies of movement equations after which their research. This strategy encouraged the improvement of recent components in arithmetic, comparable to the al­ gebraic integration and the speculation of elliptic and theta features. nonetheless, the qualitative tools of learning dynamical structures are a lot genuine. It was once Poincare who based the qualitative concept of differential equa­ tions. Poincare, figuring out qualitative tools, studied the issues of celestial mechanics and cosmology within which it really is specifically very important to appreciate the habit of trajectories of movement, i.e., the recommendations of differential equations at limitless time. specifically, starting from Poincare platforms of equations (in reference to the learn of the issues of ce­ lestial mechanics), the right-hand components of which do not rely explicitly at the self sufficient variable of time, i.e., dynamical platforms, are studied.

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