Recurrent Sets for Planar Homeomorphisms

Marcy Barge and John Franks

Chapter 19 in From Topology to Computation: Proceedings of the Smalefest, 1993, pp 186-195 from Springer

Abstract: Abstract In this article, we investigate fixed-point-free orientation-preserving homeomorphisms of ℝ2 and the recurrence of connected subsets of the plane under them. In Section 1, we give a short elementary proof that an orientation-preserving homeomorphism of the plane with a periodic point must have a fixed point.

Keywords: Periodic Point; Positive Index; Topological Disk; Additive Closure; Closed Topological Disk (search for similar items in EconPapers)
Date: 1993
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-2740-3_19

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DOI: 10.1007/978-1-4612-2740-3_19

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