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Stable ergodicity of certain linear automorphisms of the torus

Federico Rodriguez Hertz
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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 $N\leq 5$.

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Federico Rodriguez Hertz. 2002-12-26. Stable ergodicity of certain linear automorphisms of the torus. https://arxiv.org/abs/math/0212345

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