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On Boundaries of Parallelizable Regions of Flows of Free Mappings

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  • Zbigniew Leśniak

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.

Suggested Citation

  • Zbigniew Leśniak, 2007. "On Boundaries of Parallelizable Regions of Flows of Free Mappings," Abstract and Applied Analysis, Hindawi, vol. 2007, pages 1-8, October.
    • Handle: RePEc:hin:jnlaaa:031693
    DOI: 10.1155/2007/31693
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