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A periodic homeomorphism of the plane. (English) Zbl 0791.58074

West, Thelma (ed.), Continuum theory and dynamical systems. Papers of the conference/workshop on continuum theory and dynamical systems held at Lafayette, LA (USA). New York: Marcel Dekker, Inc.. Lect. Notes Pure Appl. Math. 149, 83-87 (1993).
This short article contains two proofs of a mathematical gem: The homeomorphism of the plane given by \((x,y)\mapsto (| x| - y,x)\) is periodic with period 9!
For the entire collection see [Zbl 0777.00054].

MSC:

37C25 Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics
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