Rotation vectors for minimal two torus dieomorphisms
Xiaochuan Liu


In this talk, we will look at the pointwise rotation vector for a smooth two torus diffeomorphism. We show that there exist examples where for Lebesgue almost every point of T2, the pointwise rotation vector is not well dened. That is, when we try to use the usual way to dene this number, the limit does not exist. The method we use, is a variant of Artur Avila's method to obtain a counter-example of Franks-Misiurewicz conjecture. Avila's method is a variant of Anosov-Katok method of fast approximation and conjugation. This is a joint work with A. Avila and D. Xu.