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Transactions of the American Mathematical Society

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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
MathSciNet review: 637039
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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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Keywords: Fixed point property, homeomorphism, twist homeomorphism of the annulus
Article copyright: © Copyright 1982 American Mathematical Society