Stable Ergodicity of certain linear automorphisms of the torus

Federico Rodriguez Hertz

Keywords: ergodicity | linear automorphisms | KAM | partial hyperbolicity

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 $N\leq 5$.

Anexos:

• stergf.ps