On the dynamics of homology-preserving homeomorphisms of the annulus
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Abstract:
We consider the homeomorphisms of the compact annulus $\mathbb {A} = \mathbb {S}^1 \times [-1,1]$ isotopic to the symmetry $S_{\mathbb {A}}$ which interchanges the two boundary components. We prove that if such a homeomorphism is, in some sense, conservative and twisted, then it possesses a periodic orbit of period exactly two. This can be regarded as a counterpart of the Poincaré-Birkhoff theorem in the isotopy class of $S_{\mathbb {A}}$.References
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Additional Information
- Marc Bonino
- Affiliation: Laboratoire Analyse, Géométrie et Applications (LAGA), CNRS UMR 7539, Université Paris 13, Institut Galilée, 99 Avenue J.B. Clément, 93430 Villetaneuse, France
- Email: bonino@math.univ-paris13.fr
- Received by editor(s): March 13, 2007
- Published electronically: November 4, 2008
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 361 (2009), 1903-1923
- MSC (2000): Primary 37E30; Secondary 37C25, 37E45
- DOI: https://doi.org/10.1090/S0002-9947-08-04688-6
- MathSciNet review: 2465823