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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

On the dynamics of homology-preserving homeomorphisms of the annulus


Author: Marc Bonino
Journal: Trans. Amer. Math. Soc. 361 (2009), 1903-1923
MSC (2000): Primary 37E30; Secondary 37C25, 37E45
Published electronically: November 4, 2008
MathSciNet review: 2465823
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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}}$.


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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

DOI: http://dx.doi.org/10.1090/S0002-9947-08-04688-6
Keywords: Homeomorphisms of the annulus, Poincar\'e-Birkhoff theorem, 2-periodic points
Received by editor(s): March 13, 2007
Published electronically: November 4, 2008
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.