Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-08T09:24:43.021Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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