Pseudo-prolongations in the qualitative theory of dynamical systems

This paper considers the qualitative behaviour of the flow in a neighbourhood of closed invariant sets of dynamical systems. The properties of compactness, invariance, and connectivity of pseudo-prolongations are investigated. A rather deep analysis of the flow in the vicinity of a compact invariant set of asymptotically compact phase spaces is presented. The connection of pseudo-prolongation with the first positive prolongation of T. Ura and the set of weakly elliptic points is refined.