Abstract：Consider a partially hyperbolic diffeomorphisms with an invariant splitting into three bundles - stable, center and unstable. It is already known that if the center is one dimensional, then the accessibility property persists under small perturbations of the diffeomorphisms. This was proved by Didier at the the beginning of this century. More recently Avila and Viana showed the same is true when the center is two dimensional. In this talk we will show that it is also true when the center dimension is 3. In this talk we will describe how the techniques of Avila and Viana can be adapted to the case of three-dimensional center. This talk is based in a joint work with Keith Burns and Jana Rodriguez Hertz.
