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An improvement of the Poincaré-Birkhoff fixed point theorem


Author: Patricia H. Carter
Journal: Trans. Amer. Math. Soc. 269 (1982), 285-299
MSC: Primary 54H25; Secondary 55M25, 58F99
DOI: https://doi.org/10.1090/S0002-9947-1982-0637039-0
MathSciNet review: 637039
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Abstract | References | Similar Articles | Additional Information

Abstract: If $ g$ is a twist homeomorphism of an annulus $ A$ in the plane which leaves at most one point in the interior of $ A$ fixed, then there is an essential simple closed curve in the interior of $ A$ which meets its image in at most one point; hence the annular region bounded by this simple closed curve and the inside component of the boundary of $ A$ is mapped onto either a proper subset or a proper superset of itself.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1982-0637039-0
Keywords: Fixed point property, homeomorphism, twist homeomorphism of the annulus
Article copyright: © Copyright 1982 American Mathematical Society