### 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.

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.

#### Keywords

Kerékjártó's theorem; attractor; linearization; Lyapunov function

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