Abstract and Applied Analysis
Volume 2007 (2007), Article ID 31693, 8 pages
doi:10.1155/2007/31693

On boundaries of parallelizable regions of flows of free mappings

Abstract

We are interested in the first prolongational limit set of the boundary of parallelizable regions of a given flow of the plane which has no fixed points. We prove that for every point from the boundary of a maximal parallelizable region, there exists exactly one orbit contained in this region which is a subset of the first prolongational limit set of the point. Using these uniquely determined orbits, we study the structure of maximal parallelizable regions.