Celebratio Mathematica — Kuperberg — Complete Bibliography

Complete Bibliography

Works connected to Gary Gruenhage

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M. Barge and K. Kuperberg: “Periodic points from periodic prime ends,” pp. 13–21 in Proceedings of the 1998 topology and dynamics conference (Fairfax, VA, 12–14 March 1998), vol. 23. Edited by G. Gruenhage. Topology Proc. Spring. Auburn University, 1998. MR 1743798 Zbl 0976.54047 incollection

This paper generalizes a theorem of Barge and Gillette asserting that if an orientation preserving plane homeomorphism \( F \) has a fixed prime end associated with an invariant continuum \( \Delta \) which separates the plane into exactly two domains, then \( F \) has a fixed point in \( \Delta \). The generalization goes in two directions. The Barge–Gillette theorem is proved for a continuum with more than two complementary domains if for all but one complementary domains \( U \), \( F \) has a fixed prime end in \( U \). The other generalization addresses the existence of periodic points with least period \( q \) provided certain conditions concerning \( F^q \) and periodic prime ends with the same least period are met.

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