A recurrent nonrotational homeomorphism on the annulus

Fokkink, Robbert J.; Oversteegen, Lex G.

doi:10.1090/S0002-9947-1992-1088020-8

A recurrent nonrotational homeomorphism on the annulus
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by Robbert J. Fokkink and Lex G. Oversteegen PDF

Trans. Amer. Math. Soc. 333 (1992), 865-875 Request permission

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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