Rotation sets with nonempty interior and transitivity in the universal covering

Nancy Guelman, Andres Koropecki, Fabio Armando Tal

Published 2012-08-03, updated 2013-07-09Version 2

Let $f$ be a transitive homeomorphism of the two-dimensional torus in the homotopy class of the identity. We show that a lift of $f$ to the universal covering is transitive if and only if the rotation set of the lift contains the origin in its interior.