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 is a twist homeomorphism of an annulus in the plane which leaves at most one point in the interior of fixed, then there is an essential simple closed curve in the interior of 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 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