On codimension one partially hyperbolic diffeomorphisms

We show that every codimension one partially hyperbolic diffeomorphism must support on ${\mathbb{T}}^n$. It is locally uniquely integrable and derived from a linear codimension one Anosov diffeomorphism. Moreover, this system is intrinsically ergodic, and the A. Katok’s conjecture about the existence of ergodic measures with intermediate entropies holds for it.