Removing zero Lyapunov exponents

Abstract

In an explicit family of partially hyperbolic diffeomorphisms of the torus T3, Shub and Wilkinson recently succeeded in perturbing the Lyapunov exponents of the center direction. We present here a local version of their argument, allowing one to perturb the center Lyapunov exponents of any partially hyperbolic system, in any dimension and with arbitrary dimension of the center bundle.