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

Full-text PDF Free Access

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

Keywords:
Fixed point property,
homeomorphism,
twist homeomorphism of the annulus

Article copyright:
© Copyright 1982
American Mathematical Society