Topographic Poincaré systems and comparison systems of small and high orders

On this work, we consider some qualitative questions of the theory of ordinary differential equations, on whose solutions a study of a series of dynamical systems depends. An elementary survey is given for such problems as qualitative questions of the theory of topographic Poincaré systems and more general comparison systems; problems of the existence and uniqueness of trajectories having infinitely distant points for flat systems as limit sets; elements of the qualitative theory of monotone vector fields.