Đề tài " Stable ergodicity of certain linear automorphisms of the torus "

We find a class of ergodic linear automorphisms of TN 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 TN are stably ergodic when N ≤ 5. 1. Introduction The purpose of this paper is to give sufficient conditions for a linear automorphism on the torus to be stably ergodic. By stable ergodicity we mean that any small perturbation remains ergodic. So, let a linear automorphism on the torus TN = RN /ZN be generated by a matrix A...