On the first prolongational limit set of flows of free mappings

Abstract

We consider an equivalence relation defined for a given flow of the plane which has no fixed points. We prove that the first prolongational limit set of every point from the boundary of an equivalence class is contained in the boundary of this class. Moreover, if two points lying on  two different boundary orbits of a class are contained in the same component of the complement  of an orbit of this class, then each of these two points is contained in the first prolongational  limit set of the other one.