Rotation sets with nonempty interior and transitivity in the universal covering

Abstract

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.

11 pages, 4 figures. Incorporates referee's corrections. To appear in Ergod. Th. & Dynam. Syst

References in corpus (1)

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