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

Tal, Fábio

doi:10.1090/S0002-9939-2012-11198-0

Transitivity and rotation sets with nonempty interior for homeomorphisms of the $2$-torus
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by Fábio Armando Tal PDF

Proc. Amer. Math. Soc. 140 (2012), 3567-3579 Request permission

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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