Transitivity and rotation sets with nonempty interior for homeomorphisms of the $2$-torus
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- by Fábio Armando Tal PDF
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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.References
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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
- MR Author ID: 653938
- Email: fabiotal@ime.usp.br
- 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
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 140 (2012), 3567-3579
- MSC (2010): Primary 37E45
- DOI: https://doi.org/10.1090/S0002-9939-2012-11198-0
- MathSciNet review: 2929025