Resumen de Ergodicity and Annular Homeomorphisms of the Torus

Renato B. Bortolatto, Fábio Armando Tal

• Let f : T2 → T2 be a homeomorphism homotopic to the identity and F : R2 → R2 a lift of f such that the rotation set ρ(F) is a line segment of rational slope containing a point in Q2. We prove that if f is ergodic with respect to the Lebesgue measure on the torus and the average rotation vector (with respect to same measure) does not belong to Q2 then some power of f is an annular homeomorphism.