Linearization of planar homeomorphisms with a compact attractor

Abstract

Kerékjártó proved in 1934 that a planar homeomorphism with an asymptotically stable fixed point is conjugated, on its basin of attraction, to one of the maps $z\mapsto z/2$ or $z\mapsto \overline z/2$, depending on whether $f$ preserves or reverses the orientation. We extend this result to planar homeomorphisms with a compact attractor.