Relationship of Liouville's theorem to the stability of motion of nonlinear systems of differential equations

In this paper we study the connection between the Liouville theorem for a nonautonomous system of ordinary differential equations with a resistance movement of Lyapunov. A divergence criterion for the absence of attraction for nonlinear systems of ordinary differential equations is obtained. The functions characterizing the divergence of local and unlimited condensability of trajectories of nonautonomous systems of ordinary differential equations are introduced and evaluated from the bottom.