The definition of the indices of oscillation, rotation, and wandering of nonlinear differential systems

The definitions of the indices of oscillation, rotation and wandering, similar to the Lyapunov exponents and suitable for nonlinear systems are given. Definitions are valid even when solutions are not defined on the entire positive time semiaxis. The coincidence of the new indicators with those previously known in the case of a linear system is established. Various relationships between these indicators have been studied.