CODIMENSION-1 PARTIALLY HYPERBOLIC DIFFEOMORPHISMS WITH A UNIFORMLY COMPACT CENTER FOLIATION

We consider a partially hyperbolic C-1-diffeomorphism f : M -> M with a uniformly compact f-invariant center foliation F-c. We show that if the unstable bundle is one-dimensional and oriented, then the holonomy of the center foliation vanishes everywhere, the quotient space M/F-c of the center foliation is a torus and f induces a hyperbolic automorphism on it, in particular, f is centrally transitive. We actually obtain further interesting results without restrictions on the unstable, stable and center dimension: we prove a kind of spectral decomposition for the chain recurrent set of the quotient dynamics, and we establish the existence of a holonomy-invariant family of measures on the unstable leaves (Margulis measure).