title: MOST HOMEOMORPHISMS WITH A FIXED POINT HAVE A CANTOR SET OF FIXED POINTS.
abstract: We show that, for anyn≠ 2, most orientation preserving homeomorphisms of the sphereS2nhave a Cantor set of fixed points. In other words, the set of such homeomorphisms that donothave 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 sphereS2n+1have a Cantor set of fixed points for anyn≠ 0. More generally, suppose thatMis a compact manifold of dimension > 1 and ≠ 4 and ℋ is an open set of homeomorphismsh:M→Msuch that all elements of ℋ have at least one fixed point. Then we show that most elements of ℋ have a Cantor set of fixed points.
authors.affiliation: Department of Mathematics, University of Wisconsin, 480 Lincoln Drive, Madison WI 53706, craciun@math.wisc.edu.
authors.forename: Gheorghe
authors.initials: G
authors.lastname: Craciun
keywords: Cantor set; fixed points; generic properties; homeomorphisms; manifolds