Stable ergodicity of certain linear automorphisms of the torus

Abstract

We find a class of ergodic linear automorphisms of $\mathbb{T}^N$ that are stably ergodic. This class includes all non-Anosov ergodic automorphisms when $N=4$. As a corollary, we obtain the fact that all ergodic linear automorphism of $\mathbb{T}^N$ are stably ergodic when $N\leq 5$.