Topological structure of partially hyperbolic sets with positive volume.
Abstract. We show that partially hyperbolic sets with positive volume for diffeomorphisms whose class of differentiability is higher than 1 necessarily contain stable/unstable disks. In particular, there are no partially hyperbolic horseshoes with positive, thus generalizing a classical result by Bowen for uniformly hyperbolic horseshoes. We are also able to give a good description of the topological structure of (partially) hyperbolic sets with positive volume diffeomorphisms whose class of differentiability is higher than 1. This is a joint work with V. Pinheiro.