Remote Access Transactions of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9947-1981-0626491-1
MathSciNet review: 626491
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 58F20, 28D05

Retrieve articles in all journals with MSC: 58F20, 28D05


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1981-0626491-1
Keywords: Twist map, Brouwer Translation Theorem, transitive, periodic points, covering space
Article copyright: © Copyright 1981 American Mathematical Society

American Mathematical Society