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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

  • Mladen Bestvina (a1) and Michael Handel (a2)

Abstract

We construct an area preserving homeomorphism ƒ: T2T2 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.

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References

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[F]Franks, J.. A new proof of the Brouwer plane translation theorem. Ergod, Th. & Dynam. Sys. 12 (1992) 217226.
[G]Guillou, L.. Le théorème de translation plane de Brouwer: une démonstration simplifiée menant à une nouvelle preuve du théorème de Poincaré-Birkhoff. Preprint.
[K]Kwapisz, J.. Every convex polygon with rational vertices is a rotation set. Ergod. Th. & Dynam. Sys. 12 (1992) 333339.
[MZ]Misiurewicz, M. & Ziemian, K.. Rotation sets for maps of tori. Preprint.

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

  • Mladen Bestvina (a1) and Michael Handel (a2)

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