Periodic point free homeomorphism of $T^ 2$
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- by Michael Handel PDF
- Proc. Amer. Math. Soc. 107 (1989), 511-515 Request permission
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
- John Franks, Recurrence and fixed points of surface homeomorphisms, Ergodic Theory Dynam. Systems 8$^*$ (1988), no. Charles Conley Memorial Issue, 99–107. MR 967632, DOI 10.1017/S0143385700009366 Handel, M., Zero entropy surface diffeomorphisms, preprint.
- Michael-R. Herman, Une méthode pour minorer les exposants de Lyapounov et quelques exemples montrant le caractère local d’un théorème d’Arnol′d et de Moser sur le tore de dimension $2$, Comment. Math. Helv. 58 (1983), no. 3, 453–502 (French). MR 727713, DOI 10.1007/BF02564647
Additional Information
- © Copyright 1989 American Mathematical Society
- 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