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Proceedings of the American Mathematical Society

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Periodic point free homeomorphism of $ T\sp 2$


Author: Michael Handel
Journal: Proc. Amer. Math. Soc. 107 (1989), 511-515
MSC: Primary 58F99; Secondary 57S17, 57S25
DOI: https://doi.org/10.1090/S0002-9939-1989-0965243-2
MathSciNet review: 965243
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Abstract: Suppose that $ f:{T^2} \to {T^2}$ is an orientation preserving homeomorphism of the torus that is homotopic to the identity and that has no periodic points. We show that there is a direction $ \theta $ and a number $ \rho $ such that every orbit of $ f$ has rotation number $ \rho $ in the direction $ \theta $.


References [Enhancements On Off] (What's this?)

  • [Fr] Franks, John, Recurrence and fixed points of surface homeomorphisms, to appear in Ergodic Theory and Dynamical Systems. MR 967632 (90d:58124)
  • [Ha] Handel, M., Zero entropy surface diffeomorphisms, preprint.
  • [He] Herman, M., Une methode pour minorer les exposants de Lyapounov et quelques exemples montrant le caractere local d'un theoreme d'Arnold et de Moser sur le tore de dimension 2, Comment. Math. Helv. 58 (1983), no. 3, 453-502. MR 727713 (85g:58057)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1989-0965243-2
Article copyright: © Copyright 1989 American Mathematical Society

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