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Transactions of the American Mathematical Society

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

 

 

A recurrent nonrotational homeomorphism on the annulus


Authors: Robbert J. Fokkink and Lex G. Oversteegen
Journal: Trans. Amer. Math. Soc. 333 (1992), 865-875
MSC: Primary 54H20; Secondary 58F08
MathSciNet review: 1088020
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Abstract: We construct an area- and orientation-preserving recurrent diffeomorphism on the annulus without periodic points, which is not conjugate to a rotation. The mapping is, however, semiconjugate to an irrational rotation of a circle. Our example is a counterexample to the Birkhoff Conjecture.


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DOI: https://doi.org/10.1090/S0002-9947-1992-1088020-8
Keywords: Recurrent, area preserving, annulus, almost periodic
Article copyright: © Copyright 1992 American Mathematical Society