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A simple proof of P. Carter's theorem
Author(s):
Lucien
Guillou
Journal:
Proc. Amer. Math. Soc.
125
(1997),
1555-1559.
MSC (1991):
Primary 54H20, 58F99;
Secondary 55M20, 57N05
MathSciNet review:
1372031
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Abstract:
We give a simple proof of the following result of P. Carter: Given a twist homeomorphism of an annulus with at most one fixed point in the interior of the annulus, then there exists an essential simple closed curve inside this annulus meeting its image in at most the (possible) interior fixed point.
References:
- [B]
- G. D. Birkhoff, An extension of Poincaré's last Geometric theorem, Acta Math. 47 (1925), 297-311.
- [C]
- P. H. Carter, An improvement of the Poincaré-Birkhoff fixed point theorem, Trans. AMS 269 (1982), 285-299. MR 84h:54041
- [F]
- J. Franks, Generalisations of the Poincaré-Birkhoff theorem, Ann. Math. 128 (1988), 139-151. MR 89m:54052
- [G]
- L. Guillou, Théorème de translation plane de Brouwer et généralisations du théorème de Poincaré-Birkhoff, Topology 33 (1994), 331-351. MR 95h:55003
- [K]
- B. de Kerekjarto The plane translation theorem of Brouwer and the last geometric theorem of Poincaré, Acta Sci. Math. Szeged, 4 (1928-29), 86-102.
- [LS]
- P. Le Calvez et A. Sauzet, Une preuve dynamique du théorème de translation plane de Brouwer, Expo. Math 14 (1996), 277-287.
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MSC (1991):
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Additional Information:
Lucien
Guillou
Affiliation:
Université Grenoble 1, Institut Fourier B.P. 74, 38402 Saint-Martin-d'Hères (cedex) France
Email:
lguillou@fourier.ujf-grenoble.fr
DOI:
10.1090/S0002-9939-97-03766-0
PII:
S 0002-9939(97)03766-0
Keywords:
Poincare-Birkhoff Theorem,
Brouwer Translation Theorem,
fixed point
Received by editor(s):
July 14, 1995
Received by editor(s) in revised form:
November 21, 1995
Communicated by:
Mary Rees
Copyright of article:
Copyright
1997,
American Mathematical Society
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