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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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 $.


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