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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Twist maps, coverings and Brouwer's translation theorem

Author: H. E. Winkelnkemper
Journal: Trans. Amer. Math. Soc. 267 (1981), 585-593
MSC: Primary 58F20; Secondary 28D05
MathSciNet review: 626491
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Abstract: We apply the Brouwer Translation Theorem to a class of twist maps of the annulus (which contains $ {C^1}$ area preserving maps) to show that, if $ h$ belongs to this class, then a certain set $ {\mathcal{P}_0}$ of periodic points of $ h$ cannot be dense. The definition of $ {\mathcal{P}_0}$ does not impose any a priori restrictions on the periods of the points of $ {\mathcal{P}_0}$.

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

  • [1] E. Sperner, Über die fixpunkt freien Abbildungen der Ebene, Abh. Math. Sem. Univ. Hamburg 10 (1934), 1-47.

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Keywords: Twist map, Brouwer Translation Theorem, transitive, periodic points, covering space
Article copyright: © Copyright 1981 American Mathematical Society

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