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Rotation sets are closed

Published online by Cambridge University Press:  24 October 2008

Ryuichi Ito
Ryuichi Ito
Affiliation:
University of Warwick
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Extract

The rotation number ρ of an orientation preserving homeomorphism of a circle was originally defined by Poincaré It measures the asymptotic rotation of the orbit of each point under iterations of the homeomorphism (see, for example, (2)).

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 89 , Issue 1 , January 1981 , pp. 107 - 111
Copyright
Copyright © Cambridge Philosophical Society 1981

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References

REFERENCES

(1)Newhouse, S., Palis, J. and Takens, F.Stable Families of Dynamical System I: Diffeomorphisms. Preprint, I.M.P.A., Rio, Brazil.Google Scholar
(2)Nitecki, Z.Differentiable Dynamics. M.I.T. Press, 1971.Google Scholar