Properties of Neighborhoods of Attractors of Dynamical Systems

The paper deals with the study of dynamical systems admitting compact attractors, which describe the behavior of trajectories of the system at infinity and play an important role in the qualitative theory of stability of motion. The properties of trajectories of a dynamical system in the attraction domain of the attractors and on the boundary are established by using concepts such as elliptic and weakly elliptic sets, as well as the pseudo-stability and pseudo-prolongation properties.