Periodic point free homeomorphism of
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 | References | Similar Articles | Additional Information
Abstract: Suppose that 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
and a number
such that every orbit of
has rotation number
in the direction
.
- [Fr] John Franks, Recurrence and fixed points of surface homeomorphisms, Ergodic Theory Dynam. Systems 8* (1988), no. Charles Conley Memorial Issue, 99–107. MR 967632, https://doi.org/10.1017/S0143385700009366
- [Ha] Handel, M., Zero entropy surface diffeomorphisms, preprint.
- [He] 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, https://doi.org/10.1007/BF02564647
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1989-0965243-2
Article copyright:
© Copyright 1989
American Mathematical Society