Ergodic components of partially hyperbolic systems
  This paper gives a complete classification of the possible ergodic decompositions for certain open families of volume-preserving partially hyperbolic diffeomorphisms. These families include systems with compact center leaves and perturbations of Anosov flows under conditions on the dimensions of the invariant subbundles. The paper further shows that the non-open accessibility classes form a $C^1$ lamination and gives results about the accessibility classes of non-volume-preserving systems.   Note: this document has been modified slightly from earlier preprints. The numbering of sections was changed to match the published version and an erratum has been added to the end. 
Andy Hammerlindl
math.DS