Stable ergodicity of certain linear automorphisms of the torus

Details Stable ergodicity of certain linear automorphisms of the torus Stable ergodicity of certain linear automorphisms of the torus

2002-12-26

arxiv.org/abs/math/0212345v1

Mathematics

Dynamical Systems

Scientific paper

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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