Twist maps, coverings and Brouwer’s translation theorem
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- by H. E. Winkelnkemper PDF
- Trans. Amer. Math. Soc. 267 (1981), 585-593 Request permission
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
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E. Sperner, Über die fixpunkt freien Abbildungen der Ebene, Abh. Math. Sem. Univ. Hamburg 10 (1934), 1-47.
Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 267 (1981), 585-593
- MSC: Primary 58F20; Secondary 28D05
- DOI: https://doi.org/10.1090/S0002-9947-1981-0626491-1
- MathSciNet review: 626491