Linearization of planar homeomorphisms with a compact attractor

Armengol Gasull, Jorge Groisman, Francesc Mañosas

DOI: http://dx.doi.org/10.12775/TMNA.2016.055

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.

Keywords


Kerékjártó's theorem; attractor; linearization; Lyapunov function

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