On the first prolongational limit set of flows of free mappings

Authors

  • Zbigniew Le´sniak

DOI:

https://doi.org/10.5556/j.tkjm.39.2008.19

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.

Author Biography

Zbigniew Le´sniak

nstitute of Mathematics, Pedagogical
University, Podchor\c{a}\.zych 2, 30-084 Krak\'ow, Poland.

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Published

2008-09-30

How to Cite

Le´sniak, Z. (2008). On the first prolongational limit set of flows of free mappings. Tamkang Journal of Mathematics, 39(3), 263-269. https://doi.org/10.5556/j.tkjm.39.2008.19

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Section

Papers