Topological Methods in Nonlinear Analysis

Linearization of planar homeomorphisms with a compact attractor

Armengol Gasull, Jorge Groisman, and Francesc Mañosas

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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.

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Topol. Methods Nonlinear Anal., Volume 48, Number 2 (2016), 493-506.

First available in Project Euclid: 21 December 2016

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Gasull, Armengol; Groisman, Jorge; Mañosas, Francesc. Linearization of planar homeomorphisms with a compact attractor. Topol. Methods Nonlinear Anal. 48 (2016), no. 2, 493--506. doi:10.12775/TMNA.2016.055.

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  • N.P. Bhatia and G.P. Szegö, Stability theory of dynamical systems, Reprint of the 1970 original, Classics in Mathematics, Springer–Verlag, Berlin, 2002.
  • S.S. Cairns, An elementary proof of the Jordan–Schoenflies theorem, Proc. Amer. Math. Soc. 2 (1951), 860–867.
  • A. Cima, F. Mañosas and J. Villadelprat, A Poincaré–Hopf theorem for noncompact manifolds, Topology 37 (1998), 261–277.
  • T. Homma and S. Kinoshita, On the regularity of homeomorphisms of $E^n$, J. Math. Soc. Japan 5 (1953), 365–371.
  • ––––, On a topological characterization of the dilatation in $E^3$, Osaka Math. J. 6 (1954), 135–144.
  • L.S. Husch, A topological characterization of the dilation in $E^n$, Proc. Amer. Math. Soc. 28 (1971), 234–236.
  • B. de Kerékjártó, Sur le caractère topologique des représentations conformes, C.R. Acad. Sci. Paris 198 (1934), 317–320 (in French).
  • B. von Kerékjártó, Topologische Charakterisierung der linearen Abbildungen, Acta Litt. Acad. Sei. Szeged. 6 (1934), 235–262 (in German).
  • B. Kolev, Plane Topology and Dynamical Systems, École thématique, Summer School “Systèmes Dynamiques et Topologie en Petites Dimensions", Grenoble, France, 1994, pp. 35. $\langle\mbox{cel-}00719540\rangle$
  • J. Lewowicz, Lyapunov functions and topological stability, J. Differential Equations 38 (1980), 192–209.
  • P. Ortega and F.R. Ruiz del Portal, Attractors with vanishing rotation number, J. Eur. Math. Soc. (JEMS) 13 (2011), 1569–1590.