Abstract and Applied Analysis
Volume 2007 (2007), Article ID 31693, 8 pages
Research Article

On Boundaries of Parallelizable Regions of Flows of Free Mappings

Zbigniew Leśniak

Institute of Mathematics, Pedagogical University, Podchorążych 2, Kraków 30-084, Poland

Received 7 May 2007; Revised 19 August 2007; Accepted 5 September 2007

Academic Editor: John Michael Rassias

Copyright © 2007 Zbigniew Leśniak. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.