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On generic rotationless diffeomorphisms of the annulus


Authors: Salvador Addas-Zanata and Fábio Armando Tal
Journal: Proc. Amer. Math. Soc. 138 (2010), 1023-1031
MSC (2010): Primary 37E30, 37E45; Secondary 37C20, 37C05
DOI: https://doi.org/10.1090/S0002-9939-09-10135-1
Published electronically: October 26, 2009
MathSciNet review: 2566568
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Abstract: Let $ f$ be a $ C^r$-diffeomorphism of the closed annulus $ A$ that preserves the orientation, the boundary components and the Lebesgue measure. Suppose that $ f$ has a lift $ \tilde f$ to the infinite strip $ \tilde A$ which has zero Lebesgue measure rotation number. If the rotation number of $ \tilde f$ restricted to both boundary components of $ A$ is positive, then for such a generic $ f$ ($ r\geq 16$), zero is an interior point of its rotation set. This is a partial solution to a conjecture of P. Boyland.


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Additional Information

Salvador Addas-Zanata
Affiliation: Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão 1010, Cidade Universitária, 05508-090 São Paulo, SP, Brazil
Email: sazanata@ime.usp.br

Fábio Armando Tal
Affiliation: Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão 1010, Cidade Universitária, 05508-090 São Paulo, SP, Brazil
Email: fabiotal@ime.usp.br

DOI: https://doi.org/10.1090/S0002-9939-09-10135-1
Keywords: Closed connected sets, omega limits, prime end theory, Kupka-Smale diffeomorphisms, Moser generic elliptic points
Received by editor(s): May 14, 2009
Received by editor(s) in revised form: July 22, 2009
Published electronically: October 26, 2009
Additional Notes: The first author was supported by CNPq grant 301485/03-8
The second author was supported by CNPq grant 304360/05-8
Communicated by: Bryna Kra
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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