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An area preserving homeomorphism of T2 that is fixed point free but does not move any essential simple closed curve off itself

Published online by Cambridge University Press:  19 September 2008

Mladen Bestvina  and
Michael Handel
Mladen Bestvina
Affiliation:
Department of Mathematics, UCLA, Los Angeles, CA 90024, USA
Michael Handel
Affiliation:
Department of Mathematics, CUNY, Lehman College, NY 10468, USA
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Abstract

We construct an area preserving homeomorphism ƒ: T2→T2 that is isotopic to the identity and fixed point free, but has the property that every essential simple closed curve C satisfies ƒ(C)∩C ≠ Ø. This answers a question of Guillou.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 12 , Issue 4 , December 1992 , pp. 673 - 676
Copyright
Copyright © Cambridge University Press 1992

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References

REFERENCES

[F]Franks, J.. A new proof of the Brouwer plane translation theorem. Ergod, Th. & Dynam. Sys. 12 (1992) 217–226.CrossRefGoogle Scholar
[G]Guillou, L.. Le théorème de translation plane de Brouwer: une démonstration simplifiée menant à une nouvelle preuve du théorème de Poincaré-Birkhoff. Preprint.Google Scholar
[K]Kwapisz, J.. Every convex polygon with rational vertices is a rotation set. Ergod. Th. & Dynam. Sys. 12 (1992) 333–339.CrossRefGoogle Scholar
[MZ]Misiurewicz, M. & Ziemian, K.. Rotation sets for maps of tori. Preprint.CrossRefGoogle Scholar