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

Abstract

We show that, if $f$ is a homeomorphism of the 2--torus isotopic to the identity, and its lift $\tilde{f}$ is transitive, or even if it is transitive outside of the lift of the elliptic islands, then $(0,0)$ is in the interior of the rotation set of $\tilde{f}.$ This proves a particular case of Boyland's conjecture.

Cited by in corpus (4)

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• Rotation sets with nonempty interior and transitivity in the universal covering
• Ergodicity and annular homeomorphisms of the torus
• Topologically conjugate classifications of the translation actions on low-dimensional compact connected Lie groups