Linearization of planar homeomorphisms with a compact attractor.

B. de Kerékjártó proved in [C. R. Acad. Sci., Paris 198, 317–320 (1934; Zbl 0008.22602)] that a planar homeomorphism with an asymptotically stable fixed point is conjugated, on its basin of attraction, to one of the maps z 7→ z/2 or z 7→ z/2, depending on whether f preserves or reverses the orientation. We extend this result to planar homeomorphisms with a compact attractor.