Rotation vectors for minimal two torus dieomorphisms
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 dened. That is, when we try to use the usual way to dene 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.