Study of the Complete Oscillation, Rotation, and Wandering Properties of a Differential System by the First Approximation

The concepts of complete oscillation, rotation, wandering and complete nonoscillation, nonrotation, and nonwandering of a system of differential equations (with respect to its zero solution) are introduced. A one-to-one connection between these properties and the corresponding characteristics of the system has been established. Tests for a guaranteed possibility of studying them using the first approximation system are given, as well as the examples, for which that is not possible.