Method of radial drift for qualitative study of the properties of the nonlinear dynamic systems. III. On existence of invariant closed contours

Consideration was given to existence of the invariant closed contours of th e nonlinear autonomous dynamic systems, that is, the closed contours consis ting wholly of the trajectories of dynamic systems obeying the ordinary non linear vector differential equations of an arbitrary order. The structure o f these contours was studied, and their classification was elaborated. Effi cient conditions for nonexistence and existence of the invariant contours w ere obtained. Studies were carried out using the method of radial drift.