Yu.I. Golechkov, D.V. Klimova

Asymptotic properties of trajectories of some classes of dynamical systems describing by nonlinear autonomic multidimensional differential equations are investigated in the paper. Theorems about asymptotic properties of trajectories on the basis of convergence of sets in the Hausdorff metric are obtained. The notions of limit sets of motions of nonlinear system and properties of limit sets are considered in the first part of the paper. The theorems on asymptotics of motions of dynamical systems with respect to all and part of phase variables are proved in the second and third parts of the paper. The main methods of investigation are method of Lyapunov functions and method of localization of limit sets of nonlinear dynamical systems. The examples illustrating the application of theorems are given. The obtained results may be used in the problems of stability and qualitative behavior of trajectories of dynamical systems of physics and techniques