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Transitivity and rotation sets with nonempty interior for homeomorphisms of the $ 2$-torus


Author: Fábio Armando Tal
Journal: Proc. Amer. Math. Soc. 140 (2012), 3567-3579
MSC (2010): Primary 37E45
Published electronically: February 27, 2012
MathSciNet review: 2929025
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Abstract: We show that if $ f$ is a homeomorphism of the 2-torus isotopic to the identity and its lift $ \widetilde f$ is transitive, or even if it is transitive outside the lift of the elliptic islands, then $ (0,0)$ is in the interior of the rotation set of $ \widetilde f.$ This proves a particular case of Boyland's conjecture.


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Additional Information

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/S0002-9939-2012-11198-0
Keywords: Torus homeomorphisms, rotation set, transitivity, omega limits
Received by editor(s): December 4, 2010
Received by editor(s) in revised form: April 16, 2011
Published electronically: February 27, 2012
Additional Notes: Supported by CNPq grant 304360/05-8
Communicated by: Bryna Kra
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.