A simple proof of P. Carter’s theorem
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- by Lucien Guillou PDF
- Proc. Amer. Math. Soc. 125 (1997), 1555-1559 Request permission
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
- G. D. Birkhoff, An extension of Poincaré’s last Geometric theorem, Acta Math. 47 (1925), 297–311.
- Patricia H. Carter, An improvement of the Poincaré-Birkhoff fixed point theorem, Trans. Amer. Math. Soc. 269 (1982), no. 1, 285–299. MR 637039, DOI 10.1090/S0002-9947-1982-0637039-0
- John Franks, Generalizations of the Poincaré-Birkhoff theorem, Ann. of Math. (2) 128 (1988), no. 1, 139–151. MR 951509, DOI 10.2307/1971464
- Lucien Guillou, Théorème de translation plane de Brouwer et généralisations du théorème de Poincaré-Birkhoff, Topology 33 (1994), no. 2, 331–351 (French). MR 1273787, DOI 10.1016/0040-9383(94)90016-7
- 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.
- P. Le Calvez et A. Sauzet, Une preuve dynamique du théorème de translation plane de Brouwer, Expo. Math 14 (1996), 277–287.
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
- Received by editor(s): July 14, 1995
- Received by editor(s) in revised form: November 21, 1995
- Communicated by: Mary Rees
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 1555-1559
- MSC (1991): Primary 54H20, 58F99; Secondary 55M20, 57N05
- DOI: https://doi.org/10.1090/S0002-9939-97-03766-0
- MathSciNet review: 1372031