Oscillation, rotation, and wandering exponents of solutions of differential systems

Abstract

Several characteristics of the solutions of a differential system are defined and studied from a unified standpoint, namely, they are arranged in a certain order and unite all known and some new Lyapunov characteristics describing various oscillation and wandering properties. For second-order equations, all of these characteristics coincide with each other, and for autonomous systems, the set of values of each of these characteristics contains all absolute values of the imaginary parts of eigenvalues of the operator of the system.