Margulis measure in the context of partially hyperbolic dynamics

Let $f$ be a diffeomorphism on a compact manifold $M$ and assume that the tangent bundle splits into three subbundles – stable, unstable and central - invariant under $df$ such that $df$ contracts a vector of the stable bundle, expands a vector of the unstable bundle and finally contracts/ expands to a weaker degree a vector of the central bundle. Such a diffeomorphism is called partially hyperbolic. We consider partially hyperbolic diffeomorphisms where the central bundle integrates to a compact central foliation, that is every center leaf is a compact manifold. We describe the structure and properties of these diffeomorphisms and establish the existence of a Margulis measure in this context (under some additional assumptions).