On codimension one partially hyperbolic diffeomorphisms

Abstract

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.

arXiv comment26 pages, 5 figures. Any suggestions and comments are welcome