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Arch Math 2013 Jan 13;100(1):95-99. Epub 2012 Dec 13.

Department of Mathematics, University of Wisconsin, 480 Lincoln Drive, Madison WI 53706,

We show that, for any ≠ 2, most orientation preserving homeomorphisms of the sphere have a Cantor set of fixed points. In other words, the set of such homeomorphisms that do have a Cantor set of fixed points is of the first Baire category within the set of all homeomorphisms. Similarly, most orientation reversing homeomorphisms of the sphere have a Cantor set of fixed points for any ≠ 0. Read More