Celebratio Mathematica — Kuperberg — Complete Bibliography

Complete Bibliography

Works connected to Marcy Mason Barge

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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.

Gary Gruenhage	Related
Marcy Mason Barge	Related

Geometry and topology in dynamics (Winston-Salem, NC, 9–10 October 1998 and San Antonio, TX, 13–16 January 1999). Edited by M. Barge and K. Kuperberg. Contemporary Mathematics 246. American Mathematical Society (Providence, RI), 1999. MR 1732367 Zbl 0930.00046 book