Topological Methods in Nonlinear Analysis

Linearization of planar homeomorphisms with a compact attractor

Armengol Gasull, Jorge Groisman, and Francesc Mañosas

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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.

Article information

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

Dates
First available in Project Euclid: 21 December 2016

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1482289226

Digital Object Identifier
doi:10.12775/TMNA.2016.055

Mathematical Reviews number (MathSciNet)
MR3642770

Zentralblatt MATH identifier
1364.37051

Citation

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. https://projecteuclid.org/euclid.tmna/1482289226


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