Stable ergodicity of certain linear automorphisms of the torus

Abstract

We prove that some ergodic linear automorphisms of $\T^N$ are stably ergodic, i.e. any small perturbation remains ergodic. The class of linear automorphisms we deal with includes all non-Anosov ergodic automorphisms when N=4 and so, as a corollary, we get that every ergodic linear automorphism of $\T^N$ is stably ergodic when $N\le 5$.