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

I. N. Sergeev

Matematičeskie zametki, Tome 115 (2024) no. 4, pp. 610-618

Résumé

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.

Détail

Keywords: differential system, complete oscillation, complete wandering, complete rotation, first approximation study, ball index.

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